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All Textbook Solutions for STATISTICS F/BUSINESS+ECONOMICS-TEXT

Discuss the differences between statistics as numerical facts and statistics as a discipline or field of study.Tablet PC Comparison provides a wide variety of information about tablet computers. The companys website enables consumers to easily compare different tablets using factors such as cost, type of operating system, display size, battery life, and CPU manufacturer. A sample of 10 tablet computers is shown in Table 1.6 (Tablet PC Comparison website, February 28, 2013). a. How many elements are in this data set? b. How many variables are in this data set? c. Which variables are categorical and which variables are quantitative? d. What type of measurement scale is used for each of the variables?Refer to Table 1.6. a. What is the average cost for the tablets? b. Compare the average cost of tablets with a Windows operating system to the average cost of tablets with an Android operating system. c. What percentage of tablets use a CPU manufactured by TI OMAP? d. What percentage of tablets use an Android operating system? TABLE 1.6 PRODUCT INFORMATION FOR 10 TABLET COMPUTERS Tablet Cost () Operating System Display Size (inches) Battery Life (hours) CPU Manufacturer Acer Iconia W510 599 Windows 10.1 8.5 Intel Amazon Kindle Fire HD 299 Android 8.9 9 TI OMAP Apple iPad 4 499 iOS 9.7 11 Apple HP Envy X2 860 Windows 11.6 8 Intel Lenovo ThinkPad Tablet 668 Windows 10.1 10.5 Intel Microsoft Surface Pro 899 Windows 10.6 4 Intel Motorola Droid XYboard 530 Android 10.1 9 TI OMAP Samsung Ativ Smart PC 590 Windows 11.6 7 Intel Samsung Galaxy Tab 525 Android 10.1 10 Nvidia Sony Tablet S 360 Android 9.4 8 Nvidia Table 1.7 shows data for eight cordless telephones (Consumer Reports, November 2012). The Overall Score, a measure of the overall quality for the cordless telephone, ranges from 0 to 100. Voice Quality has possible ratings of poor, fair, good, very good, and excellent. Talk Time is the manufacturers claim of how long the handset can be used when it is fully charged. a. How many elements are in this data set? b. For the variables Price, Overall Score, Voice Quality, Handset on Base, and TalkTime, which variables are categorical and which variables are quantitative? c. What scale of measurement is used for each variable?Refer to the data set in Table 1.7. a. What is the average price for the cordless telephones? b. What is the average talk time for the cordless telephones? c. What percentage of the cordless telephones have a voice quality of excellent? d. What percentage of the cordless telephones have a handset on the base? TABLE 1.7 DATA FOR EIGHT CORDLESS TELEPHONES Brand Model Price () Overall Score Voice Quality Handset on Base Talk Time (Hours) ATT CL84100 60 73 Excellent Yes 7 ATT TL92271 80 70 Very Good No 7 Panasonic 4773B 100 78 Very Good Yes 13 Panasonic 6592T 70 72 Very Good No 13 Uniden D2997 45 70 Very Good No 10 Uniden D1788 80 73 Very Good Yes 7 Vtech DS6521 60 72 Excellent No 7 Vtech CS6649 50 72 Very Good Yes 7 J.D. Power and Associates surveys new automobile owners to learn about the quality of recently purchased vehicles. The following questions were asked in the J.D. Power Initial Quality Survey, May 2012. a. Did you purchase or lease the vehicle? b. What price did you pay? c. What is the overall attractiveness of your vehicles exterior? (Unacceptable, Average, Outstanding, or Truly Exceptional) d. What is your average miles per gallon? e. What is your overall rating of your new vehicle? (1- to 10-point scale with 1 Unacceptable and 10 Truly Exceptional) Comment on whether each question provides categorical or quantitative data.The Kroger Company is one of the largest grocery retailers in the United States, with over 2000 grocery stores across the country. Kroger uses an online customer opinion questionnaire to obtain performance data about its products and services and learn about what motivates its customers (Kroger website. April 2012). In the survey, Kroger customers were asked if they would be willing to pay more for products that had each of the following four characteristics. The four questions were: Would you pay more for products that have a brand name? products that are environmentally friendly? products that are organic? products that have been recommended by others ? For each question, the customers had the option of responding Yes if they would pay more or No if they would not pay more. a. Are the data collected by Kroger in this example categorical or quantitative? b. What measurement scale is used?The Tennessean, an online newspaper located in Nashville, Tennessee, conducts a daily poll to obtain reader opinions on a variety of current issues. In a recent poll, 762 readers responded to the following question: If a constitutional amendment to ban a state income tax is placed on the ballot in Tennessee, would you want it to pass? Possible responses A were Yes, No, or Not Sure (The Tennessean website, February 15, 2013). a. What was the sample size for this poll? b. Are the data categorical or quantitative? c. Would it make more sense to use averages or percentages as a summary of the data for this question? d. Of the respondents, 67% said Yes, they would want it to pass. How many individuals provided this response?The Commerce Department reported receiving the following applications for the Malcolm Baldrige National Quality Award: 23 from large manufacturing firms, 18 from large service firms, and 30 from small businesses. a. Is type of business a categorical or quantitative variable? b. What percentage of the applications came from small businesses?The Bureau of Transportation Statistics Omnibus Household Survey is conducted annually and serves as an information source for the U.S. Department of Transportation. In one part of the survey the person being interviewed was asked to respond to the following statement: Drivers of motor vehicles should be allowed to talk on a hand-held cell phone while driving." Possible responses were strongly agree, somewhat agree, somewhat disagree, and strongly disagree. Forty-four respondents said that they strongly agree with this statement. 130 said that they somewhat agree. 165 said they somewhat disagree, and 741 said they strongly disagree with this statement (Bureau of Transportation website. August 2010). a. Do the responses for this statement provide categorical or quantitative data? b. Would it make more sense to use averages or percentages as a summary of the responses for this statement? c. What percentage of respondents strongly agree with allowing drivers of motor vehicles to talk on a hand-held cell phone while driving? d. Do the results indicate general support for or against allowing drivers of motor vehicles to talk on a hand-held cell phone while driving?In a Gallup telephone survey conducted on April 9-10,2013, the person being interviewed was asked if he would vote for a law in his state that would increase the gas tax up to 20 cents a gallon, with the new gas tax money going to improve roads and bridges and build more mass transportation in his state. Possible responses were vote for, vote against, and no opinion. Two hundred ninety five respondents said they would vote for the law, 672 said they would vote against the law, and 51 said they had no opinion (Gallup website, June 14. 2013). a. Do the responses for this question provide categorical or quantitative data? b. What was the sample size for this Gallup poll? c. What percentage of respondents would vote for a law increasing the gas tax? d. Do the results indicate general support for or against increasing the gas tax to improve roads and bridges and build more mass transportation?The Hawaii Visitors Bureau collects data on visitors to Hawaii. The following questions were among 16 asked in a questionnaire handed out to passengers during incoming airline flights. This trip to Hawaii is my: 1st, 2nd, 3rd, 4th, etc. The primary reason for this trip is: (10 categories, including vacation, convention, honeymoon) Where I plan to stay: (11 categories, including hotel, apartment, relatives, camping) Total days in Hawaii a. What is the population being studied? b. Is the use of a questionnaire a good way to reach the population of passengers on incoming airline flights? c. Comment on each of the four questions in terms of whether it will provide categorical or quantitative data.Figure 1.7 provides a bar chart showing the annual revenue for Google from 2004 to 2014. (The Wall Street Journal, August 19, 2014). a. What is the variable of interest? b. Arc the data categorical or quantitative? c. Arc the data time series or cross-sectional? d. Comment on the trend in Google revenue over time. FIGURE 1.7 GOOGLE REVENUE The following data show the number of rental cars in service for three rental car companies: Hertz, Avis, and Dollar. The data are for the years 2007-2010 and are in thousands of vehicles (Auto Rental News website, May 15, 2011). Company 2007 Cars in Service (1000s) 2010 2008 2009 Hertz 327 311 286 290 Dollar 167 140 106 108 Avis 204 220 300 270 a.Construct a time series graph for the years 2007 to 2010 showing the number of rental cars in service for each company. Show the time series for all three companies on the same graph. b.Comment on who appears to be the market share leader and how the market shares are changing over time. c.Construct a bar chart showing rental cars in service for 2010. Is this chart based on cross-sectional or time series data?Every year, the U.S. Coast Guard collects data and compiles statistics on reported recreational boating accidents. These statistics are derived from accident reports that are filed by the owners/operators of recreational vessels involved in accidents. In 2009, 4730 recreational boating accident reports were filed. Figure 1.8 provides a bar chart summarizing the number of accident reports that were filed each month (U.S. Coast Guards Boating Safety Division website, August 2010). a. Are the data categorical or quantitative? b. Are the data time series or cross-sectional? c. In what month were the most accident reports filed? Approximately how many? d. There were 61 accident reports filed in January and 76 accident reports filed in December. What percentage of the total number of accident reports for the year were filed in these two months? Does this seem reasonable? e. Comment on the overall shape of the bar graph. FIGURE 1.8 NUMBER OF RECREATIONAL BOATING ACCIDENTS A manager of a large corporation recommends a 10,000 raise be given to keep a valued subordinate from moving to another company. What internal and external sources of data might be used to decide whether such a salary increase is appropriate?A random telephone survey of 1021 adults (aged 18 and older) was conducted by Opinion Research Corporation on behalf of CompleteTax, an online tax preparation and e-filing service. The survey results showed that 684 of those surveyed planned to file their taxes electronically (CompleteTax Tax Prep Survey 2010). a. Develop a descriptive statistic that can be used to estimate the percentage of all taxpayers who file electronically. b. The survey reported that the most frequently used method for preparing the tax return is to hire an accountant or professional tax preparer. If 60% of the people surveyed had their tax return prepared this way. how many people used an accountant or professional tax preparer? c. Other methods that the person filing the return often used include manual preparation. use of an online tax service, and use of a software tax program. Would the data for the method for preparing the tax return be considered categorical or quantitative?A Bloomberg Businessweek North American subscriber study collected data from a sample of 2861 subscribers. Fifty-nine percent of the respondents indicated an annual income of 75,000 or more, and 50% reported having an American Express credit card. a. What is the population of interest in this study? b. Is annual income a categorical or quantitative variable? c. Is ownership of an American Express card a categorical or quantitative variable? d. Does this study involve cross-sectional or time series data? e. Describe any statistical inferences Bloomberg Businessweek might make on the basis of the survey.A survey of 131 investment managers in Barrons Big Money poll revealed the following: 43% of managers classified themselves as bullish or very bullish on the stock market. The average expected return over the next 12 months for equities was 11.2%. 21% selected health care as the sector most likely to lead the market in the next 12 months. When asked to estimate how long it would take for technology and telecom stocks to resume sustainable growth, the managers average response was 2.5 years. a. Cite two descriptive statistics. b. Make an inference about the population of all investment managers concerning the average return expected on equities over the next 12 months. c. Make an inference about the length of time it will take for technology and telecom stocks to resume sustainable growth.A seven-year medical research study reported that women whose mothers took the drug DES during pregnancy were twice as likely to develop tissue abnormalities that might lead to cancer as were women whose mothers did not take the drug. a. This study compared two populations. What were the populations? b. Do you suppose the data were obtained in a survey or an experiment? c. For the population of women whose mothers took the drug DES during pregnancy, a sample of 3980 women showed that 63 developed tissue abnormalities that might lead to cancer. Provide a descriptive statistic that could be used to estimate the number of women out of 1000 in this population who have tissue abnormalities. d. For the population of women whose mothers did not take the drug DES during pregnancy, what is the estimate of the number of women out of 1000 who would be expected to have tissue abnormalities? e. Medical studies often use a relatively large sample (in this case. 3980). Why ?A survey conducted by Better Homes and Gardens Real Estate LLC showed that one in five U.S. homeowners have either moved from their home or would like to move because their neighborhood or community isnt ideal for their lifestyle (Better Homes and Gardens Real Estate website, September 26,2013). The top lifestyle priorities of respondents when searching for their next home include ease of commuting by car, access to health and safety services, family-friendly neighborhood, availability of retail stores, access to cultural activities, public transportation access, and nightlife and restaurant access. Suppose a real estate agency in Denver. Colorado, hired you to conduct a similar study to determine the top lifestyle priorities for clients that currently have a home listed for sale with the agency or have hired the agency to help them locate a new home. a. What is the population for the survey you will be conducting? b.How would you collect the data for this study?Pew Research Center is a nonpartisan polling organization that provides information about issues, attitudes, and trends shaping America. In a poll. Pew researchers found that 47% of American adult respondents reported getting at least some local news on their cell phone or tablet computer (Pew Research website. May 14, 2011). Further findings showed that 42% of respondents who own cell phones or tablet computers use those devices to check local weather reports and 37% use the devices to find local restaurants or other businesses. a. One statistic concerned using cell phones or tablet computers for local news. What population is that finding applicable to? b. Another statistic concerned using cell phones or tablet computers to check local weather reports and to find local restaurants. What population is this finding applicable to? c. Do you think the Pew researchers conducted a census or a sample survey to obtain their results? Why? d. If you were a restaurant owner, would you find these results interesting? Why ? How could you take advantage of this information?A sample of midterm grades for five students showed the following results: 72, 65, 82, 90, 76. Which of the following statements are correct, and which should be challenged as being too generalized? a. The average midterm grade for the sample of five students is 77. b. The average midterm grade for all students who took the exam is 77. c. An estimate of the average midterm grade for all students who took the exam is 77. d. More than half of the students who take this exam will score between 70 and 85. e. If five other students are included in the sample, their grades will be between 65 and 90.Table 1.8 shows a data set containing information for 25 of the shadow stocks tracked by the American Association of Individual Investors. Shadow stocks are common stocks of smaller companies that are not closely followed by Wall Street analysts. The data set is also on the website that accompanies the text in the DATAfile named Shadow02. a. How many variables are in the data set? b. Which of the variables are categorical and which are quantitative? c. For the Exchange variable, show the frequency and the percent frequency for AMEX, NYSE, and OTC. Construct a bar graph similar to Figure 1.4 for the Exchange variable. d. Show the frequency distribution for the Gross Profit Margin using the five intervals: 0-14.9, 15-29.9, 30-44.9, 45-59.9, and 60-74.9. Construct a histogram similar to Figure 1.5. e. What is the average price/earnings ratio? TABLE 1.8 DATA SET FOR 25 SHADOW STOCKS Company Exchange Ticker Symbol Market Cap ( millions) Price/Earnings Ratio (.ross Profit Margin (%) DeWolfe Companies AMEX DWL 36.4 8.4 36.7 North Coast Energy OTC NCEB 52.5 6.2 59.3 Hansen Natural Corp. OTC HANS 41.1 14.6 44.8 MarineMax, Inc. NYSE HZO 111.5 7.2 23.8 Nanometrics Incorporated OTC NANO 228.6 38.0 53.3 TeamStaff, Inc. OTC TSTF 92.1 33.5 4.1 Environmental Tectonics AMEX ETC 51.1 35.8 35.9 Measurement Specialties AMEX MSS 101.8 26.8 37.6 SEMCO Energy, Inc. NYSE SEN 193.4 18.7 23.6 Party City Corporation OTC PCTY 97.2 15.9 36.4 Embrex, Inc. OTC EMBX 136.5 18.9 59.5 Tech/Ops Sevcon, Inc. AMEX TO 23.2 20.7 35.7 ARCADES NV OTC ARCAF 173.4 8.8 9.6 Qiao Xing Universal Tele. OTC XING 64.3 22.1 30.8 Energy West Incorporated OTC EWST 29.1 9.7 16.3 Barnwell Industries. Inc. AMEX BRN 27.3 7.4 73.4 Innodata Corporation OTC INOD 66.1 11.0 29.6 Medical Action Industries OTC MDCI 13(7.1 26.9 30.6 Instrumentarium Corp. OTC INMRY 240.9 3.6 52.1 Petroleum Development OTC PETD 95.9 6.1 19.4 Drexler Technology Corp. OTC DRXR 233.6 45.6 53.6 Gerber Childrenswear Inc. NYSE GCW 126.9 7.9 25.8 Gaiam, Inc. OTC GAIA 295.5 68.2 60.7 Artesian Resources Corp. OTC ARTNA 62.8 20.5 45.5 York Water Company OTC YORW 92.2 22.9 74.2 Methods 1. The response to a question has three alternatives: A, B, and C. A sample of 120 responses provides 60 A, 24 B, and 36 C. Show the frequency and relative frequency distributions.A partial relative frequency distribution is given. Class Relative Frequency A .22 B .18 C .40 D a. What is the relative frequency of class D? b. The total sample size is 200. What is the frequency of class D? c. Show the frequency distribution. d. Show the percent frequency distribution.A questionnaire provides 58 Yes, 42 No, and 20 no-opinion answers. a. In the construction of a pie chart, how many degrees would be in the section of the pie showing the Yes answers? b. How many degrees would be in the section of the pie showing the No answers? c. Construct a pie chart. d. Construct a bar chart.for the 20102011 viewing season, the top five syndicated programs were wheel of Fortune (WoF), Two and Half Men (THM), Jeopardy (Jep), Judge Judy (JJ), and the oprah winfrey Show (OWS) (Nielsen Media Research website, April 16, 2012). Data indicating the preferred shows for a sample of 50 viewers follow. a. Are these data categorical or quantitative? b. Provide frequency and percent frequency distributions. c. Construct a bar chart and a pie chart. d. On the basis of the sample, which television show has the largest viewing audience? Which one is second?In alphabetical order, the six most common last names in the United States are brown, Johnson, Jones, Miller, Smith, and Williams (The world Almanac, 2012). Assume that a sample of 50 individuals with one of these last names provided the following data. Summarize the data by constructing the following: a. Relative and percent frequency distributions b. A bar chart c. A pie chart d. based on these data, what are the three most common last names?Nielsen Media Research provided the list of the 25 top-rated single shows in television history (The World Almanac, 2012). The following data show the television network that produced each of these 25 top-rated shows. a. Construct a frequency distribution, percent frequency distribution, and bar chart for the data. b. which network or networks have done the best in terms of presenting top-rated television shows? Compare the performance of ABC, CBS, and NBC.The Canmark Research Center Airport Customer Satisfaction Survey uses an online questionnaire to provide airlines and airports with customer satisfaction ratings for all aspects of the customers flight experience (airportsurvey website, July 2012). After completing a flight, customers receive an e-mail asking them to go to the website and rate a variety of factors, including the reservation process, the check-in process, luggage policy, cleanliness of gate area, service by flight attendants, food/beverage selection, on-time arrival, and so on. A five-point scale, with Excellent (E), Very Good (V), Good (G), Fair (F), and Poor (P), is used to record customer ratings. Assume that passengers on a delta Airlines flight from Myrtle beach, South Carolina, to Atlanta, Georgia, provided the following ratings for the question, Please rate the airline based on your overall experience with this flight. The sample ratings are shown below. a. Use a percent frequency distribution and a bar chart to summarize these data. What do these summaries indicate about the overall customer satisfaction with the Delta flight? b. The online survey questionnaire enabled respondents to explain any aspect of the flight that failed to meet expectations. Would this be helpful information to a manager looking for ways to improve the overall customer satisfaction on Delta flights? Explain.Data for a sample of 55 members of the Baseball Hall of Fame in Cooperstown, New York, are shown here. Each observation indicates the primary position played by the Hall of Famers: pitcher (P), catcher (H), 1st base (1), 2nd base (2), 3rd base (3), shortstop (S), left field (L), center field (C), and right field (R). a. Construct frequency and relative frequency distributions to summarize the data. b. What position provides the most Hall of Famers? c. What position provides the fewest Hall of Famers? d. What outfield position (L, C, or R) provides the most Hall of Famers? e. Compare infielders (1, 2, 3, and S) to outfielders (L, C, and R).Nearly 1.8 million bachelors degrees and over 750,000 masters degrees are awarded annually by U.S. postsecondary institutions (National Center for Education Statistics website, November, 2014). The department of Education tracks the field of study for these graduates in the following categories: Business (b), Computer Sciences and Engineering (CSE), Education (E), Humanities (H), Natural Sciences and Mathematics (NSM), Social and Behavioral Sciences (SbS), and Other (O). Consider the following samples of 100 graduates: Bachelors Degree Field of Study Masters Degree Field of Study a. Provide a percent frequency distribution of field of study for each degree. b. Construct a bar chart for field of study for each degree. c. What is the lowest percentage field of study for each degree? d. What is the highest percentage field of study for each degree? e. Which field of study has the largest increase in percentage from bachelors to masters?VirtualTourist provides ratings for hotels throughout the world. Ratings provided by 649 guests at the Sheraton Anaheim Hotel, located near the Disneyland Resort in Anaheim, California, can be found in the DATAfile named HotelRatings (VirtualTourist website, February 25, 2013). Possible responses were Excellent, Very Good, Average, Poor, and Terrible. a. Construct a frequency distribution. b. Construct a percent frequency distribution. c. Construct a bar chart for the percent frequency distribution. d. Comment on how guests rate their stay at the Sheraton Anaheim Hotel. e. Results for 1679 guests who stayed at Disneys Grand Californian provided the following frequency distribution. Rating Frequency Excellent 807 Very Good 521 Average 200 Poor 107 Terrible 44 Compare the ratings for Disneys Grand Californian with the results obtained for the Sheraton Anaheim Hotel.Consider the following data. a. Develop a frequency distribution using classes of 1214, 1517, 1820, 2123, and 2426. b. Develop a relative frequency distribution and a percent frequency distribution using the classes in part (a).Consider the following frequency distribution. Class Frequency 10-19 10 20-29 14 30-39 17 40-49 7 50-59 2 Construct a cumulative frequency distribution and a cumulative relative frequency distribution.Construct a histogram for the data in exercise 12.Consider the following data. a. Construct a dot plot. b. Construct a frequency distribution. c. Construct a percent frequency distribution.Construct a stem-and-leaf display for the following data. 11.3 9.6 10.4 7.5 8.3 10.5 10.0 9.3 8.1 7.7 7.5 8.4 6.3 8.8 Construct a stem-and-leaf display for the following data. Use a leaf unit of 10. 1161 1206 1478 1300 1604 1725 1361 1422 1221 1378 1623 1426 1557 1730 1706 1689 Applications A doctors office staff studied the waiting times for patients who arrive at the office with a request for emergency service. The following data with waiting times in minutes were collected over a one-month period. 2 5 10 12 4 4 5 17 11 8 9 8 12 21 6 8 7 13 18 3 Use classes of 04, 59, and so on in the following: a. Show the frequency distribution. b. Show the relative frequency distribution. c. Show the cumulative frequency distribution. d. Show the cumulative relative frequency distribution. e. What proportion of patients needing emergency service wait 9 minutes or less?CBSSports.com developed the Total Player Ratings system to rate players in the National Basketball Association (NBA) based upon various offensive and defensive statistics. The following data show the average number of points scored per game (PPG) for 50 players with the highest ratings for a portion of the 20122013 NBA season (CBSSports.com website, February 25, 2013). Use classes starting at 10 and ending at 30 in increments of 2 for PPG in the following. a. Show the frequency distribution. b. Show the relative frequency distribution. c. Show the cumulative percent frequency distribution. d. Develop a histogram for the average number of points scored per game. e. Do the data appear to be skewed? Explain. f. What percentage of the players averaged at least 20 points per game?Based on the tons handled in a year, the ports listed below are the 25 busiest ports in the United States (The 2013 World Almanac). a. What is the largest number of tons handled? What is the smallest number of tons handled? b. Using a class width of 25, develop a frequency distribution of the data starting with 2549.9, 5074.9, 7599.9, and so on. c. Prepare a histogram. Interpret the histogram.The London School of Economics and the Harvard Business School conducted a study of how chief executive officers (CEOs) spend their day. The study found that CEOs spend on average about 18 hours per week in meetings, not including conference calls, business meals, and public events (The Wall Street Journal, February 14, 2012). Shown below is the time spent per week in meetings (hours) for a sample of 25 CEOs. a. What is the least amount of time spent per week on meetings? The highest? b. Use a class width of two hours to prepare a frequency distribution and a percent frequency distribution for the data. c. Prepare a histogram and comment on the shape of the distribution.Fortune provides a list of Americas largest corporations based on annual revenue. Shown below are the 50 largest corporations, with annual revenue expressed in billions of dollars (CNN Money website, January 15, 2010). Summarize the data by constructing the following: a. A frequency distribution (classes 049, 5099, 100149, and so on). b. A relative frequency distribution. c. A cumulative frequency distribution. d. A cumulative relative frequency distribution. e. what do these distributions tell you about the annual revenue of the largest corporations in America? f. Show a histogram. Comment on the shape of the distribution. g. what is the largest corporation in America and what is its annual revenue?entrepreneur magazine ranks franchises using performance measures such as growth rate, number of locations, startup costs, and financial stability. The number of locations for the top 20 U.S. franchises follow (The world Almanac, 2012). Use classes 04999, 50009999, 10,00014,999 and so forth to answer the following questions. a. Construct a frequency distribution and a percent frequency distribution of the number of U.S. locations for these top-ranked franchises. b. Construct a histogram of these data. c. Comment on the shape of the distribution.The DATAfile EngineeringSalary contains the median starting salary and median midcareer salary (measured 10 years after graduation) for graduates from 19 engineering schools (The Wall Street Journal website, November 2014). Develop a stem-and-leaf display for both the median starting salary and the median mid-career salary. Comment on any differences you observe.Each year America.EDU ranks the best paying college degrees in America. The following data show the median starting salary, the mid-career salary, and the percentage increase from starting salary to mid-career salary for the 20 college degrees with the highest mid-career salary (America.EDU website, August 29, 2013). a. Using a class width of 10, construct a histogram for the percentage increase in the starting salary. b. Comment on the shape of the distribution. c. Develop a stem-and-leaf display for the percentage increase in the starting salary. d. What are the primary advantages of the stem-and-leaf display as compared to the histogram?The 2011 Cincinnati Flying Pig Half-Marathon (13.1 miles) had 10,897 finishers (Cincinnati Flying Pig Marathon website). The following data show the ages for a sample of 40 half-marathoners. 49 33 40 37 56 44 46 57 55 32 50 52 43 64 40 46 24 30 37 43 31 43 50 36 61 27 44 35 31 43 52 43 66 31 50 72 26 59 21 47 a. Construct a stretched stem-and-leaf display. b. Which age group had the largest number of runners? c. Which age occurred most frequently?The following data are for 30 observations involving two categorical variables, x and y. The categories for x are A, B, and C; the categories for y are 1 and 2. a. Develop a crosstabulation for the data, with x as the row variable and y as the column variable. b. Compute the row percentages. c. Compute the column percentages. d. What is the relationship, if any, between x and y?The following observations are for two quantitative variables, x and y. a. develop a crosstabulation for the data, with x as the row variable and y as the column variable. For x use classes of 1029, 3049, and so on; for y use classes of 4059, 6079, and so on. b. Compute the row percentages. c. Compute the column percentages. d. What is the relationship, if any, between x and y?The Daytona 500 is a 500-mile automobile race held annually at the Daytona International Speedway in Daytona beach, Florida. The following crosstabulation shows the automobile make by average speed of the 25 winners from 1988 to 2012 (The 2013 world Almanac). a. Compute the row percentages. b. What percentage of winners driving a Chevrolet won with an average speed of at least 150 miles per hour? c. Compute the column percentages. d. What percentage of winning average speeds 160169.9 miles per hour were Chevrolets?The following crosstabulation shows the average speed of the 25 winners by year of the Daytona 500 automobile race (The 2013 World Almanac). a. Calculate the row percentages. b. what is the apparent relationship between average winning speed and year? What might be the cause of this apparent relationship?Recently, management at Oak Tree Golf Course received a few complaints about the condition of the greens. Several players complained that the greens are too fast. Rather than react to the comments of just a few, the Golf Association conducted a survey of 100 male and 100 female golfers. The survey results are summarized here. a. Combine these two crosstabulations into one with Male and Female as the row labels and Too Fast and Fine as the column labels. Which group shows the highest percentage saying that the greens are too fast? b. Refer to the initial crosstabulations. For those players with low handicaps (better players), which group (male or female) shows the higher percentage saying the greens are too fast? c. Refer to the initial crosstabulations. For those players with higher handicaps, which group (male or female) shows the higher percentage saying the greens are too fast? d. What conclusions can you draw about the preferences of men and women concerning the speed of the greens? Are the conclusions you draw from part (a) as compared with parts (b) and (c) consistent? Explain any apparent inconsistencies.The following crosstabulation shows the number of households (1000s) in each of the four regions of the United States and the number of households at each income level (U.S. Census Bureau website, August 2013). a. Compute the row percentages and identify the percent frequency distributions of income for households in each region. b. What percentage of households in the west region have an income level of 50,000 or more? What percentage of households in the South region have an income level of 50,000 or more? c. Construct percent frequency histograms for each region of households. do any relationships between regions and income level appear to be evident in your findings? d. Compute the column percentages. What information do the column percentages provide? e. What percent of households with a household income of 100,000 and over are from the South region? What percentage of households from the South region have a household income of 100,000 and over? Why are these two percentages different?Each year Forbes ranks the worlds most valuable brands. A portion of the data for 82 of the brands in the 2013 Forbes list is shown in Table 2.12 (Forbes website, February, 2014). The data set includes the following variables: Brand:The name of the brand. Industry:The type of industry associated with the brand, labeled Automotive Luxury, Consumer Packaged Goods, Financial Services, Other, Technology. Brand Value ( billions): A measure of the brands value in billions of dollars developed by Forbes based on a variety of financial information about the brand. 1-Yr Value Change (%): The percentage change in the value of the brand over the previous year. Brand Revenue ( billions): The total revenue in billions of dollars for the brand. a. Prepare a crosstabulation of the data on Industry (rows) and Brand Value ( billions). Use classes of 010, 1020, 2030, 3040, 4050, and 5060 for Brand Value ( billions). b. Prepare a frequency distribution for the data on Industry. c. Prepare a frequency distribution for the data on Brand Value ( billions). Table 2.12 DATA FOR 82 OF THE MOST VALUABLE BRANDS d. How has the crosstabulation helped in preparing the frequency distributions in parts (b) and (c)? e. What conclusions can you draw about the type of industry and the brand value?Refer to Table 2.12. a. Prepare a crosstabulation of the data on Industry (rows) and Brand Revenue ( billions). Use class intervals of 25 starting at 0 for Brand Revenue ( billions). b. Prepare a frequency distribution for the data on Brand Revenue ( billions). c. What conclusions can you draw about the type of industry and the brand revenue? d. Prepare a crosstabulation of the data on Industry (rows) and the 1-Yr Value Change (%). Use class intervals of 20 starting at 60 for 1-Yr Value Change (%). e. Prepare a frequency distribution for the data on 1-Yr Value Change (%). f. What conclusions can you draw about the type of industry and the 1-year change in value? Table 2.12 DATA FOR 82 OF THE MOST VALUABLE BRANDS The U.S. Department of Energys Fuel Economy Guide provides fuel efficiency data for cars and trucks (Fuel Economy website, September, 2012). A portion of the data for 149 compact, midsize, and large cars is shown in Table 2.13. The data set contains the following variables: Size: Compact, Midsize, and Large Displacement: Engine size in liters Cylinders: Number of cylinders in the engine Drive: All wheel (A), front wheel (F), and rear wheel (R) Fuel Type: Premium (P) or regular (R) fuel City MPG: Fuel efficiency rating for city driving in terms of miles per gallon Hwy MPG: Fuel efficiency rating for highway driving in terms of miles per gallon The complete data set is contained in the file named FuelData2012. a. Prepare a crosstabulation of the data on Size (rows) and Hwy MPG (columns). Use classes of 1519, 2024, 2529, 3034, 3539, and 4044 for Hwy MPG. b. Comment on the relationship between Size and Hwy MPG. c. Prepare a crosstabulation of the data on Drive (rows) and City MPG (columns). Use classes of 1014, 1519, 2024, 2529, 3034, and 3539, and 4044 for City MPG. d. Comment on the relationship between Drive and City MPG. e. Prepare a crosstabulation of the data on Fuel Type (rows) and City MPG (columns). Use classes of 1014, 1519, 2024, 2529, 3034, 3539, and 4044 for City MPG. f. Comment on the relationship between Fuel Type and City MPG.The following 20 observations are for two quantitative variables, x and y. a. Develop a scatter diagram for the relationship between x and y. b. What is the relationship, if any, between x and y?Consider the following data on two categorical variables. The first variable, x, can take on values A, B, C, or D. The second variable, y, can take on values I or II. The following table gives the frequency with which each combination occurs. a. Construct a side-by-side bar chart with x on the horizontal axis. b. Comment on the relationship between x and y.The following crosstabulation summarizes the data for two categorical variables, x and y. The variable x can take on values low, medium, or high and the variable y can take on values yes or no. a. Compute the row percentages. b. Construct a stacked percent frequency bar chart with x on the horizontal axis.A study on driving speed (miles per hour) and fuel efficiency (miles per gallon) for midsize automobiles resulted in the following data: Driving Speed 30 50 40 55 30 25 60 25 50 55 Fuel Efficiency 28 25 25 23 30 32 21 35 26 25 a. Construct a scatter diagram with driving speed on the horizontal axis and fuel efficiency on the vertical axis. b. Comment on any apparent relationship between these two variables.The Current Results website lists the average annual high and low temperatures (degrees Fahrenheit) and average annual snowfall (inches) for fifty-one major U.S. cities, based on data from 1981 to 2010. The data are contained in the file Snow. for example, the average low temperature for Columbus, Ohio is 44 degrees and the average annual snowfall is 27.5 inches. a. Construct a scatter diagram with the average annual low temperature on the horizontal axis and the average annual snowfall on the vertical axis. b. Does there appear to be any relationship between these two variables? c. Based on the scatter diagram, comment on any data points that seem to be unusual.People often wait until middle age to worry about having a healthy heart. However, recent studies have shown that earlier monitoring of risk factors such as blood pressure can be very beneficial (The Wall Street Journal, January 10, 2012). Having higher than normal blood pressure, a condition known as hypertension, is a major risk factor for heart disease. Suppose a large sample of individuals of various ages and gender was selected and that each individuals blood pressure was measured to determine if they have hypertension. For the sample data, the following table shows the percentage of individuals with hypertension. a. Develop a side-by-side bar chart with age on the horizontal axis, the percentage of individuals with hypertension on the vertical axis, and side-by-side bars based on gender. b. What does the display you developed in part (a), indicate about hypertension and age? c. Comment on differences by gender.Smartphones are advanced mobile phones with Internet, photo, and music and video capability (The Pew Research Center, Internet American Life Project, 2011). The following survey results show smartphone ownership by age. a. Construct a stacked bar chart to display the above survey data on type of mobile phone ownership. Use age category as the variable on the horizontal axis. b. Comment on the relationship between age and smartphone ownership. c. How would you expect the results of this survey to be different if conducted in 2021?The Northwest regional manager of an outdoor equipment retailer conducted a study to determine how managers at three store locations are using their time. A summary of the results are shown in the following table. a. Create a stacked bar chart with store location on the horizontal axis and percentage of time spent on each task on the vertical axis. b. Create a side-by-side bar chart with store location on the horizontal axis and side-by-side bars of the percentage of time spent on each task. c. Which type of bar chart (stacked or side-by-side) do you prefer for these data? Why?Approximately 1.5 million high school students take the SAT each year and nearly 80% of the college and universities without open admissions policies use SAT scores in making admission decisions (College Board, March 2009). The current version of the SAT includes three parts: reading comprehension, mathematics, and writing. A perfect combined score for all three parts is 2400. A sample of SAT scores for the combined three-part SAT are as follows: a. Show a frequency distribution and histogram. Begin with the first class starting at 800 and use a class width of 200. b. Comment on the shape of the distribution. c. What other observations can be made about the SAT scores based on the tabular and graphical summaries?The DATAfile MedianHousehold contains the median household income for a family with two earners for each of the fifty states (American Community Survey, 2013). a. Construct a frequency and a percent frequency distribution of median household income. Begin the first class at 65.0 and use a class width of 5. b. Construct a histogram. c. Comment on the shape of the distribution. d. Which state has the highest median income for two-earner households? e. Which state has the lowest median income for two-earner households?Data showing the population by state in millions of people follow (The World Almanac, 2012). a. Develop a frequency distribution, a percent frequency distribution, and a histogram. Use a class width of 2.5 million. b. Does there appear to be any skewness in the distribution? Explain. c. What observations can you make about the population of the 50 states?A startup companys ability to gain funding is a key to success. The funds raised (in millions of dollars) by 50 startup companies appear below (The Wall Street Journal, March 10, 2011). a. Construct a stem-and-leaf display. b. Comment on the display.Consumer complaints are frequently reported to the Better Business Bureau. In 2011, the industries with the most complaints to the Better Business Bureau were banks; cable and satellite television companies; collection agencies; cellular phone providers; and new car dealerships (USA Today, April 16, 2012). The results for a sample of 200 complaints are contained in the file BBB. a. Show the frequency and percent frequency of complaints by industry. b. Construct a bar chart of the percent frequency distribution. c. Which industry had the highest number of complaints? d. Comment on the percentage frequency distribution for complaints.The term Beta refers to a measure of a stocks price volatility relative to the stock market as a whole. A Beta of 1 means the stocks price moves exactly with the market. A Beta of 1.6 means the stocks price would increase by 1.6% for an increase of 1% in the stock market. A larger Beta means the stock price is more volatile. The Betas for the stocks of the companies that make up the Dow Jones Industrial Average are shown in Table 2.17 (Yahoo Finance, November 2014). a. Construct a frequency distribution and percent frequency distribution. b. Construct a histogram. c. Comment on the shape of the distribution. d. Which stock has the highest Beta? Which has the lowest Beta?The U.S. Census Bureau serves as the leading source of quantitative data about the nations people and economy. The following crosstabulation shows the number of households (1000s) and the household income by the level of education for heads of household having received a high school degree or more education (U.S. Census Bureau website. 2013). a. Construct a percent frequency distribution for the level of education variable. What percentage of heads of households have a masters or doctoral degree? b. Construct a percent frequency distribution for the household income variable. What percentage of households have an income of 50,000 or more? c. Convert the entries in the crosstabulation into column percentages. Compare the level of education of households with a household income of under 25,000 to the level of education of households with a household income of 100,000 or more. Comment on any other items of interest when reviewing the crosstabulation showing column percentages.western University has only one womens softball scholarship remaining for the coming year. The final two players that western is considering are Allison fealey and Emily Janson. The coaching staff has concluded that the speed and defensive skills are virtually identical for the two players, and that the final decision will be based on which player has the best batting average. Crosstabulations of each players batting performance in their junior and senior years of high school are as follows: A players batting average is computed by dividing the number of hits a player has by the total number of at-bats. batting averages are represented as a decimal number with three places after the decimal. a. Calculate the batting average for each player in her junior year. Then calculate the batting average of each player in her senior year. Using this analysis, which player should be awarded the scholarship? Explain. b. Combine or aggregate the data for the junior and senior years into one crosstabulation as follows: Player Outcome Fealey Jamon Hit No Hit Total At-Bats Calculate each players batting average for the combined two years. Using this analysis, which player should be awarded the scholarship? Explain. c. Are the recommendations you made in parts (a) and (b) consistent? Explain any apparent inconsistencies.Fortune magazine publishes an annual survey of the 100 best companies to work for. The data in the DATAfile named FortuneBest100 shows the rank, company name, the size of the company, and the percentage job growth for full-time employees for 98 of the Fortune 100 companies for which percentage job growth data were available (Fortune magazine website, February 25, 2013). The column labeled Rank shows the rank of the company in the Fortune 100 list; the column labeled Size indicates whether the company is a small company (less than 2500 employees), a midsized company (2500 to 10,000 employees), or a large company (more than 10,000 employees); and the column labeled Growth Rate (%) shows the percentage growth rate for full-time employees. a. Construct a crosstabulation with Job Growth (%) as the row variable and Size as the column variable. Use classes starting at -10 and ending at 70 in increments of 10 for Growth Rate (%). b. Show the frequency distribution for Job Growth (%) and the frequency distribution for Size. c. Using the crosstabulation constructed in part (a), develop a crosstabulation showing column percentages. d. Using the crosstabulation constructed in part (a), develop a crosstabulation showing row percentages. e. Comment on the relationship between the percentage job growth for full-time employees and the size of the company.Table 2.18 shows a portion of the data for a sample of 103 private colleges and universities. The complete data set is contained in the file named Colleges. The data include the name of the college or university, the year the institution was founded, the tuition and fees (not including room and board) for the most recent academic year, and the percentage of full time, first-time bachelors degree-seeking undergraduate students who obtain their degree in six years or less (The world Almanac, 2012). a. Construct a crosstabulation with Year Founded as the row variable and Tuition Fees as the column variable. Use classes starting with 1600 and ending with 2000 in increments of 50 for Year Founded. For Tuition Fees, use classes starting with 1 and ending 45000 in increments of 5000. b. Compute the row percentages for the crosstabulation in part (a). c. What relationship, if any, do you notice between Year Founded and Tuition Fees? TABLE 2.18 DATA FOR A SAMPLE OF PRIVATE COLLEGES AND UNIVERSITIES Refer to the data set in Table 2.18. a. Construct a crosstabulation with Year Founded as the row variable and % Graduate as the column variable. Use classes starting with 1600 and ending with 2000 in increments of 50 for Year Founded. for % Graduate, use classes starting with 35% and ending with 100% in increments of 5%. b. Compute the row percentages for your crosstabulation in part (a). c. Comment on any relationship between the variables. TABLE 2.18 DATA FOR A SAMPLE OF PRIVATE COLLEGES AND UNIVERSITIES Refer to the data set in Table 2.18. a. Construct a scatter diagram to show the relationship between Year Founded and Tuition Fees. b. Comment on any relationship between the variables. TABLE 2.18 DATA FOR A SAMPLE OF PRIVATE COLLEGES AND UNIVERSITIES Refer to the data set in Table 2.18. a. Prepare a scatter diagram to show the relationship between Tuition Fees and % Graduate. b. Comment on any relationship between the variables. TABLE 2.18 DATA FOR A SAMPLE OF PRIVATE COLLEGES AND UNIVERSITIES Google has changed its strategy with regard to how much and over which media it invests in advertising. The following table shows Googles marketing budget in millions of dollars for 2008 and 2011 (The Wall Street Journal, March 27, 2012). 2008 2011 Internet 26.0 123.3 Newspaper, etc. 4.0 20.7 Television 0.0 69.3 a. Construct a side-by-side bar chart with year as the variable on the horizontal axis. Comment on any trend in the display. b. Convert the above table to percentage allocation for each year. Construct a stacked bar chart with year as the variable on the horizontal axis. c. Is the display in part (a) or part (b) more insightful? Explain.A zoo has categorized its visitors into three categories: member, school, and general. The member category refers to visitors who pay an annual fee to support the zoo. Members receive certain benefits such as discounts on merchandise and trips planned by the zoo. The school category includes faculty and students from day care and elementary and secondary schools; these visitors generally receive a discounted rate. The general category includes all other visitors. The zoo has been concerned about a recent drop in attendance. To help better understand attendance and membership, a zoo staff member has collected the following data: a. Construct a bar chart of total attendance over time. Comment on any trend in the data. b. Construct a side-by-side bar chart showing attendance by visitor category with year as the variable on the horizontal axis. c. Comment on what is happening to zoo attendance based on the charts from parts (a) and (b).Pelican Stores Pelican Stores, a division of National Clothing, is a chain of womens apparel stores operating throughout the country. The chain recently ran a promotion in which discount Coupons were sent to customers of other National Clothing stores. Data collected for a sample of 100 in-store credit card transactions at Pelican Stores during one day while the promotion was running are contained in the file named PelicanStores. Table 2.19 shows a portion of the data set. The Proprietary Card method of payment refers to charges made using a National Clothing charge card. Customers who made a purchase using a discount coupon are referred to as promotional customers and customers who made a purchase but TABLE 2.19 DATA FOR A SAMPLE OF 100 CREDIT CARD PURCHASES AT PELICAN STORES did not use a discount coupon are referred to as regular customers. Because the promotional coupons were not sent to regular Pelican Stores customers, management considers the sales made to people presenting the promotional coupons as sales it would not otherwise make. Of course. Pelican also hopes that the promotional customers will continue to shop at its stores. Most of the variables shown in Table 2.19 are self-explanatory, but two of the variables require some clarification. Items The total number of items purchased Net Sales The total amount () charged to the credit card Pelicans management would like to use this sample data to learn about its customer base and to evaluate the promotion involving discount coupons. Managerial Report Use the tabular and graphical methods of descriptive statistics to help management develop a customer profile and to evaluate the promotional campaign. At a minimum, your report should include the following: 1. Percent frequency distribution for key variables. 2. A bar chart or pie chart showing the number of customer purchases attributable to the method of payment. 3. A crosstabulation of type of customer (regular or promotional) versus net sales. Comment on any similarities or differences present. 4. A scatter diagram to explore the relationship between net sales and customer age.Motion Picture Industry The motion picture industry is a competitive business. More than 50 studios produce a total of 300 to 400 new motion pictures each year, and the financial success of each motion picture varies considerably. The opening weekend gross sales (millions), the total gross sales (millions). the number of theaters the movie was shown in. and the number of weeks TABLE 2.20 PERFORMANCE DATA FOR 10 MOTION PICTURES the motion picture was in release are common variables used to measure the success of a motion picture. Data collected for the top 100 motion pictures produced in 2011 are contained in the file named 2011 Movies (Box Office Mojo. March 17,2012). Table 2.20 shows the data for the first 10 motion pictures in this file. Managerial Report Use the tabular and graphical methods of descriptive statistics to learn how these variables contribute to the success of a motion picture. Include the following in your report. 1. Tabular and graphical summaries for each of the four variables along with a discussion of what each summary tells us about the motion picture industry. 2. A scatter diagram to explore the relationship between Total Gross Sales and Opening Weekend Gross Sales. Discuss. 3. A scatter diagram to explore the relationship between Total Gross Sales and Number of Theaters. Discuss. 4. A scatter diagram to explore the relationship between Total Gross Sales and Number of Weeks in Release. Discuss.Queen City Cincinnati, Ohio, also known as the Queen City, has a population of approximately 298.000 and is the third largest city in the state of Ohio. The Cincinnati metropolitan area has a population of about 2.2 million. The city is governed by a mayor and a nine-member city council. The city manager, who is responsible for the day-to-day operation of the city, reports to the mayor and city council. The city manager recently created the Office of Performance and Data Analytics with the goal of improving the efficiency of city operations. TABLE 2.21 ANNUAL EXPENDITURES FOR QUEEN CITY (FIRST FOUR ENTRIES) One of the first tasks of this new office is to review the previous years expenditures. The file QueenCity contains data on the previous years expenditures, including the following: Department The number of the department incurring the expenditure Department Description The name of the department incurring the description Category The category of the expenditure Fund The fund to which the expenditure was charged Expenditure The dollar amount of the expense Table 2.21 shows the first four entries of the 5427 expenditures for the year. The city manager would like to use this data to better understand how the citys budget is being spent. Managerial Report Use tabular and graphical methods of descriptive statistics to help the city manager get a better understanding of how the city is spending its funding. Your report should include the following: 1. Tables and/or graphical displays that show the amount of expenditures by category and percentage of total expenditures by category. 2. A table that shows the amount of expenditures by department and the percentage of total expenditures by department. Combine any department with less than 1% into a category named Other. 3. A table that shows the amount of expenditures by fund and the percentage of total expenditures by fund. Combine any fund with less than 1 % into a category named Other.Consider a sample with data values of 10, 20, 12, 17, and 16. Compute the mean and median.Consider a sample with data values of 10, 20, 21, 17, 16, and 12. Compute the mean and median.Consider the following data and corresponding weights. xi Weight (wi) 3.2 6 2.0 3 2.5 2 5.0 8 a. Compute the weighted mean. b. Compute the sample mean of the four data values without weighting. Note the difference in the results provided by the two computations.Consider the following data. Period Rate of Return (%) 1 6.0 2 8.0 3 4.0 4 2.0 5 5.4 What is the mean growth rate over these five periods?Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Compute the 20th, 25th, 65th, and 75th percentiles.Consider a sample with data values of 53, 55, 70, 58, 64, 57, 53, 69, 57, 68, and 53. Compute the mean, median, and mode.The average number of minutes Americans commute to work is 27.7 minutes (Sterlings Best Places, April 13, 2012). The average commute time in minutes for 48 cities are as follows: a. What is the mean commute time for these 48 cities? b. Compute the median commute time. c. Compute the mode. d. Compute the third quartile.The Wall Street Journal reported that the median salary for middle-level manager jobs was approximately 85,000 (The Wall Street Journal, August 6, 2013). Suppose that an independent study of middle-level managers employed at companies located in Atlanta, Georgia, was conducted to compare the salaries of managers working at firms in Atlanta to the national average. The following data show the salary, in thousands of dollars, for a sample of 15 middle-level managers. 108 83 106 73 53 85 80 63 67 75 124 55 93 118 77 a. Compute the median salary for the sample of 15 middle-level managers. How does the median for this group compare to the median reported by The Wall Street Journal? b. Compute the mean annual salary and discuss how and why it differs from the median computed in part (a). c. Compute the first and third quartiles.Which companies spend the most money on advertising? Business insider maintains a list of the top-spending companies. In 2014, Procter gamble spent more than any other company, a whopping 5 billion. In second place was Comcast, which spent 3.08 billion (Business Insider website, December 2014). The top 12 companies and the amount each spent on advertising in billions of dollars are as follows. a. What is the mean amount spent on advertising? b. What is the median amount spent on advertising? c. What are the first and third quartiles?Over a nine-month period, OutdoorGearLab tested hardshell jackets designed for ice climbing, mountaineering, and backpacking. Based on the breathability, durability, versatility, features, mobility, and weight of each jacket, an overall rating ranging from 0 (lowest) to 100 (highest) was assigned to each jacket tested. The following data show the results for 20 top-of-the-line jackets (OutdoorGearLab website, February 27, 2013). a. Compute the mean, median, and mode. b. Compute the first and third quartiles. c. Compute and interpret the 90th percentile.According to the National Education Association (NEA), teachers generally spend more than 40 hours each week working on instructional duties (NEA website, April 2012). The following data show the number of hours worked per week for a sample of 13 high school science teachers and a sample of 11 high school English teachers. a. What is the median number of hours worked per week for the sample of 13 high school science teachers? b. What is the median number of hours worked per week for the sample of 11 high school English teachers? c. Which group has the higher median number of hours worked per week? What is the difference between the median number of hours worked per week?The Big Bang Theory, a situation comedy featuring Johnny Galecki, Jim Parsons, and Kaley Cuoco-Sweeting, is one of the most watched programs on network television. The first two episodes for the 20112012 season premiered on September 22, 2011; the first episode attracted 14.1 million viewers and the second episode attracted 14.7 million viewers. The following table shows the number of viewers in millions for the first 21 episodes of the 20112012 season (The Big Bang Theory website, April 17, 2012). a. Compute the minimum and maximum number of viewers. b. Compute the mean, median, and mode. c. Compute the first and third quartiles. d. Has viewership grown or declined over the 20112012 season? Discuss.In automobile mileage and gasoline-consumption testing, 13 automobiles were road tested for 300 miles in both city and highway driving conditions. The following data were recorded for miles-per-gallon performance. Use the mean, median, and mode to make a statement about the difference in performance for city and highway driving.The data contained in the file named StateUnemp show the unemployment rate in March 2011 and the unemployment rate in March 2012 for every state and the District of Columbia (Bureau of Labor Statistics website, April 20, 2012). To compare unemployment rates in March 2011 with unemployment rates in March 2012, compute the first quartile, the median, and the third quartile for the March 2011 unemployment data and the March 2012 unemployment data. What do these statistics suggest about the change in unemployment rates across the states?Martinez Auto Supplies has retail stores located in eight cities in California. The price they charge for a particular product in each city varies because of differing competitive conditions. For instance, the price they charge for a case of a popular brand of motor oil in each city follows. Also shown are the number of cases that Martinez Auto sold last quarter in each city. City Price () Sales (cases) Bakersfield 34.99 501 Los Angeles 38.99 1425 Modesto 36.00 294 Oakland 33.59 882 Sacramento 40.99 715 San Diego 38.59 1088 San Francisco 39.59 1644 San Jose 37.99 819 Compute the average sales price per case for this product during the last quarter.The grade point average for college students is based on a weighted mean computation. For most colleges, the grades are given the following data values: A (4), B (3), C (2), D (1), and F (0). After 60 credit hours of course work, a student at State University earned 9 credit hours of A, 15 credit hours of B, 33 credit hours of C, and 3 credit hours of D. a. Compute the students grade point average. b. Students at State University must maintain a 2.5 grade point average for their first 60 credit hours of course work in order to be admitted to the business college. Will this student be admitted?The following table shows the total return and the number of funds for four categories of mutual funds. Type of Fund Number of Funds Total Return (%) Domestic Equity 9191 4.65 International Equity 2621 18.15 Specialty Stock 1419 11.36 Hybrid 2900 6.75 a. Using the number of funds as weights, compute the weighted average total return for these mutual funds. b. Is there any difficulty associated with using the number of funds as the weights in computing the weighted average total return in part (a)? Discuss. What else might be used for weights? c. Suppose you invested 10,000 in this group of mutual funds and diversified the investment by placing 2000 in Domestic Equity funds, 4000 in International Equity funds, 3000 in Specialty Stock funds, and 1000 in Hybrid funds. What is the expected return on the portfolio?Based on a survey of masters programs in business administration, magazines such as U.S. News World Report rank U.S. business schools. These types of rankings are based in part on surveys of business school deans and corporate recruiters. Each survey respondent is asked to rate the overall academic quality of the masters program on a scale from 1 marginal to 5 outstanding. Use the sample of responses shown below to compute the weighted mean score for the business school deans and the corporate recruiters. Discuss. Quality Assessment Business School Deans Corporate Recruiters 5 44 31 4 66 34 3 60 43 2 10 12 1 0 0 Annual revenue for Corning Supplies grew by 5.5% in 2010, 1.1% in 2011, 3.5% in 2012, 1.1% in 2013, and 1.8% in 2014. What is the mean growth annual rate over this period?Suppose that at the beginning of 2004 you invested 10,000 in the Stivers mutual fund and 5000 in the Trippi mutual fund. The value of each investment at the end of each subsequent year is provided in the table below. Which mutual fund performed better? Year Stivers Trippi 2004 11,000 5,600 2005 12,000 6,300 2006 13,000 6,900 2007 14,000 7,600 2008 15,000 8,500 2009 16,000 9,200 2010 17,000 9,900 2011 18,000 10,600 If an asset declines in value from 5000 to 3500 over nine years, what is the mean annual growth rate in the assets value over these nine years?The current value of a company is 25 million. If the value of the company six year ago was 10 million, what is the companys mean annual growth rate over the past six years?Consider a sample with data values of 10, 20, 12, 17, and 16. Compute the range and interquartile range.Consider a sample with data values of 10, 20, 12, 17, and 16. Compute the variance and standard deviation.Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Compute the range, interquartile range, variance, and standard deviation.Data collected by the Oil Price information Service from more than 90,000 gasoline and convenience stores throughout the U.S. showed that the average price for a gallon of unleaded gasoline was 3.28 (MSN Auto website, February 2, 2014). The following data show the price per gallon () for a sample of 20 gasoline and convenience stores located in San Francisco. a. Use the sample data to estimate the mean price for a gallon of unleaded gasoline in San Francisco. b. Compute the sample standard deviation. c. Compare the mean price per gallon for the sample data to the national average price. What conclusions can you draw about the cost living in San Francisco?The results of a search to find the least expensive round-trip flights to Atlanta and Salt Lake City from 14 major U.S. cities are shown in the following table. The departure date was June 20, 2012, and the return date was June 27, 2012. a. Compute the mean price for a round-trip flight into Atlanta and the mean price for a round-trip flight into Salt Lake City. is Atlanta less expensive to fly into than Salt Lake City? if so, what could explain this difference? b. Compute the range, variance, and standard deviation for the two samples. What does this information tell you about the prices for flights into these two cities?The Australian Open is the first of the four grand Slam professional tennis events held each year. victoria Azarenka beat Maria Sharapova to win the 2012 Australian Open womens title (Washington Post, January 27, 2012). During the tournament Ms. Azarenkas serve speed reached 178 kilometers per hour. A list of the 20 Womens Singles serve speed leaders for the 2012 Australian Open is provided below. a. Compute the mean, variance, and standard deviation for the serve speeds. b. A similar sample of the 20 Womens Singles serve speed leaders for the 2011 Wimbledon tournament showed a sample mean serve speed of 182.5 kilometers per hour. The variance and standard deviation were 33.3 and 5.77, respectively. Discuss any difference between the serve speeds in the Australian Open and the Wimbledon womens tournaments.The Los Angeles times regularly reports the air quality index for various areas of Southern California. A sample of air quality index values for Pomona provided the following data: 28, 42, 58, 48, 45, 55, 60, 49, and 50. a. Compute the range and interquartile range. b. Compute the sample variance and sample standard deviation. c. A sample of air quality index readings for Anaheim provided a sample mean of 48.5, a sample variance of 136, and a sample standard deviation of 11.66. What comparisons can you make between the air quality in Pomona and that in Anaheim on the basis of these descriptive statistics?The following data were used to construct the histograms of the number of days required to fill orders for Dawson Supply, inc., and J.C. Clark Distributors (see Figure 3.2). Use the range and standard deviation to support the previous observation that Dawson Supply provides the more consistent and reliable delivery times.The results of Accounting Principals latest Workonomix survey indicate the average American worker spends 1092 on coffee annually (the Consumerist, January 20, 2012). To determine if there are any differences in coffee expenditures by age group, samples of 10 consumers were selected for three age groups (1834, 3544, and 45 and Older). The dollar amount each consumer in the sample spent last year on coffee is provided below. 1834 3544 45 and Older 1355 969 1135 115 434 956 1456 1792 400 2045 1500 1374 1621 1277 1244 994 1056 825 1937 1922 763 1200 1350 1192 1567 1586 1305 1390 1415 1510 a. Compute the mean, variance, and standard deviation for the each of these three samples. b. What observations can be made based on these data?Advertising age annually compiles a list of the 100 companies that spend the most on advertising. Consumer-goods company Procter gamble has often topped the list, spending billions of dollars annually (Advertising Age website, March 12, 2013). Consider the data found in the file Advertising. it contains annual advertising expenditures for a sample of 20 companies in the automotive sector and 20 companies in the department store sector. a. What is the mean advertising spent for each sector? b. What is the standard deviation for each sector? c. What is the range of advertising spent for each sector? d. What is the interquartile range for each sector? e. Based on this sample and your answers to parts (a) to (d), comment on any differences in the advertising spending in the automotive companies versus the department store companies.Scores turned in by an amateur golfer at the Bonita Fairways golf Course in Bonita Springs, Florida, during 2011 and 2012 are as follows: a. Use the mean and standard deviation to evaluate the golfers performance over the two-year period. b. What is the primary difference in performance between 2011 and 2012? What improvement, if any, can be seen in the 2012 scores?The following times were recorded by the quarter-mile and mile runners of a university track team (times are in minutes). After viewing this sample of running times, one of the coaches commented that the quarter-milers turned in the more consistent times. Use the standard deviation and the coefficient of variation to summarize the variability in the data. Does the use of the coefficient of variation indicate that the coachs statement should be qualified?Consider a sample with data values of 10, 20, 12, 17, and 16. Compute the z-score for each of the five observations.Consider a sample with a mean of 500 and a standard deviation of 100. What are the z-scores for the following data values: 520, 650, 500, 450, and 280?Consider a sample with a mean of 30 and a standard deviation of 5. Use Chebyshevs theorem to determine the percentage of the data within each of the following ranges: a. 20 to 40 b. 15 to 45 c. 22 to 38 d. 18 to 42 e. 12 to 48 Suppose the data have a bell-shaped distribution with a mean of 30 and a standard deviation of 5. Use the empirical rule to determine the percentage of data within each of the following ranges: a. 20 to 40 b. 15 to 45 c. 25 to 35 The results of a national survey showed that on average, adults sleep 6.9 hours per night. Suppose that the standard deviation is 1.2 hours. a. Use Chebyshevs theorem to calculate the percentage of individuals who sleep between 4.5 and 9.3 hours. b. Use Chebyshevs theorem to calculate the percentage of individuals who sleep between 3.9 and 9.9 hours. c. Assume that the number of hours of sleep follows a bell-shaped distribution. Use the empirical rule to calculate the percentage of individuals who sleep between 4.5 and 9.3 hours per day. How does this result compare to the value that you obtained using Chebyshevs theorem in part (a)?The energy information Administration reported that the mean retail price per gallon of regular grade gasoline was 3.43 (Energy Information Administration, July 2012). Suppose that the standard deviation was .10 and that the retail price per gallon has a bell-shaped distribution. a. What percentage of regular grade gasoline sold between 3.33 and 3.53 per gallon? b. What percentage of regular grade gasoline sold between 3.33 and 3.63 per gallon? c. What percentage of regular grade gasoline sold for more than 3.63 per gallon?The Graduate Management Admission Test (GMAT) is a standardized exam used by many universities as part of the assessment for admission to graduate study in business. The average GMAT score is 547 (Magoosh website, January 5, 2015). Assume that GMAT scores are bell-shaped with a standard deviation of 100. a. What percentage of GMAT scores are 647 or higher? b. What percentage of GMAT scores are 747 or higher? c. What percentage of GMAT scores are between 447 and 547? d. What percentage of GMAT scores are between 347 and 647?Many families in California are using backyard structures for home offices, art studios, and hobby areas as well as for additional storage. Suppose that the mean price for a customized wooden, shingled backyard structure is 3100. Assume that the standard deviation is 1200. a. What is the z-score for a backyard structure costing 2300? b. What is the z-score for a backyard structure costing 4900? c. interpret the z-scores in parts (a) and (b). Comment on whether either should be considered an outlier. d. if the cost for a backyard shed-office combination built in Albany, California, is 13,000, should this structure be considered an outlier? explain.According to a Los Angeles Times study of more than 1 million medical dispatches from 2007 to 2012, the 911 response time for medical aid varies dramatically across Los Angeles (La Times website, November 2012). Under national standards adopted by the Los Angeles Fire Department, rescuers are supposed to arrive within six minutes to almost all medical emergencies. But the Times analysis found that in affluent hillside communities stretching from Griffith Park to Pacific Palisades, firefighters failed to hit that mark nearly 85% of the time. The following data show the response times, in minutes, for 10 emergency calls in the Griffith Park neighborhood. 11.8 10.3 10.7 10.6 11.5 8.3 10.5 10.9 10.7 11.2 Based on this sample of ten response times, compute the descriptive statistics in parts (a) and (b) and then answer the questions in parts (c) and (d): a. Mean, median, and mode b. Range and standard deviation c. Should the response time of 8.3 minutes be considered an outlier in comparison to the other response times? d. Do the response times indicate that the city is meeting the national standards? Should the city consider making changes to its response strategies? Would adding more stations to areas in the city be a practical solution? Discuss.A sample of 10 NCAA college basketball game scores provided the following data. a. Compute the mean and standard deviation for the points scored by the winning team. b. Assume that the points scored by the winning teams for all NCAA games follow a bell-shaped distribution. Using the mean and standard deviation found in part (a), estimate the percentage of all NCAA games in which the winning team scores 84 or more points. Estimate the percentage of NCAA games in which the winning team scores more than 90 points. c. Compute the mean and standard deviation for the winning margin. Do the data contain outliers? Explain.The Wall Street Journal reported that Walmart Stores inc. is planning to lay off 2300 employees at its Sams Club warehouse unit. Approximately half of the layoffs will be hourly employees (The Wall Street Journal, January 2526, 2014). Suppose the following data represent the percentage of hourly employees laid off for 15 Sams Club stores. 55 56 44 43 44 56 60 62 57 45 36 38 50 69 65 a. Compute the mean and median percentage of hourly employees being laid off at these stores. b. Compute the first and third quartiles. c. Compute the range and interquartile range. d. Compute the variance and standard deviation. e. Do the data contain any outliers? f. Based on the sample data, does it appear that Walmart is meeting its goal for reducing the number of hourly employees?Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Provide the five-number summary for the data.47E 48E A data set has a first quartile of 42 and a third quartile of 50. Compute the lower and upper limits for the corresponding box plot. Should a data value of 65 be considered an outlier?Naples, Florida, hosts a half-marathon (13.1-mile race) in January each year. The event attracts top runners from throughout the United States as well as from around the world. In January 2009, 22 men and 31 women entered the 1924 age class. Finish times in minutes are as follows (Naples Daily News, January 19, 2009). Times are shown in order of finish. a. George Towett of Marietta, Georgia, finished in first place for the men and Lauren Wald of Gainesville, Florida, finished in first place for the women. Compare the first-place finish times for men and women. If the 53 men and women runners had competed as one group, in what place would Lauren have finished? b. What is the median time for men and women runners? Compare men and women runners based on their median times. c. Provide a five-number summary for both the men and the women. d. Are there outliers in either group? e. Show the box plots for the two groups. Did men or women have the most variation in finish times? Explain.Annual sales, in millions of dollars, for 21 pharmaceutical companies follow. a. Provide a five-number summary. b. Compute the lower and upper limits. c. Do the data contain any outliers? d. Johnson Johnsons sales are the largest on the list at 14,138 million. Suppose a data entry error (a transposition) had been made and the sales had been entered as 41,138 million. Would the method of detecting outliers in part (c) identify this problem and allow for correction of the data entry error? e. Show a box plot.Consumer Reports provided overall customer satisfaction scores for ATT, Sprint, T-Mobile, and Verizon cell-phone services in major metropolitan areas throughout the United States. The rating for each service reflects the overall customer satisfaction considering a variety of factors such as cost, connectivity problems, dropped calls, static interference, and customer support. A satisfaction scale from 0 to 100 was used with 0 indicating completely dissatisfied and 100 indicating completely satisfied. The ratings for the four cell-phone services in 20 metropolitan areas are as shown (Consumer Reports, January 2009). a. Consider T-Mobile first. What is the median rating? b. Develop a five-number summary for the T-Mobile service. c. Are there outliers for T-Mobile? explain. d. Repeat parts (b) and (c) for the other three cell-phone services. e. Show the box plots for the four cell-phone services on one graph. Discuss what a comparison of the box plots tells about the four services. Which service did Consumer Reports recommend as being best in terms of overall customer satisfaction?Fortune magazines list of the worlds most admired companies for 2014 is provided in the data contained in the DATAfile named AdmiredCompanies (Fortune, March 17, 2014). The data in the column labelled Return shows the one-year total return (%) for the top ranked 50 companies. For the same time period the SP average return was 18.4%. a. Compute the median return for the top ranked 50 companies. b. What percentage of the top-ranked 50 companies had a one-year return greater than the SP average return? c. Develop the five-number summary for the data. d. Are there any outliers? e. Develop a box plot for the one-year total return.The Bureau of Transportation Statistics keeps track of all border crossings through ports of entry along the U.S.-Canadian and U.S.-Mexican borders. The data contained in the DATAfile named BorderCrossings show the most recently published figures for the number of personal vehicle crossings (rounded to the nearest 1000) at the 50 busiest ports of entry during the month of August (U.S. Department of Transportation website, February 28, 2013). a. What are the mean and median number of crossings for these ports of entry? b. What are the first and third quartiles? c. Provide a five-number summary. d. Do the data contain any outliers? Show a box plot.Five observations taken for two variables follow. a. Develop a scatter diagram with x on the horizontal axis. b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? c. Compute and interpret the sample covariance. d. Compute and interpret the sample correlation coefficient.Five observations taken for two variables follow. a. Develop a scatter diagram for these data. b. What does the scatter diagram indicate about a relationship between x and y? c. Compute and interpret the sample covariance. d. Compute and interpret the sample correlation coefficient.Ten major college football bowl games were played in January 2010, with the University of Alabama beating the University of Texas 37 to 21 to become the national champion of college football. The results of the 10 bowl games follow (USA today, January 8, 2010). The predicted winning point margin was based on Las Vegas betting odds approximately one week before the bowl games were played. For example, Auburn was predicted to beat Northwestern in the Outback Bowl by five points. The actual winning point margin for Auburn was three points. A negative predicted winning point margin means that the team that won the bowl game was an underdog and expected to lose. For example, in the Rose Bowl, Ohio State was a two-point underdog to Oregon and ended up winning by nine points. a. Develop a scatter diagram with predicted point margin on the horizontal axis. b. What is the relationship between predicted and actual point margins? c. Compute and interpret the sample covariance. d. Compute the sample correlation coefficient. What does this value indicate about the relationship between the Las Vegas predicted point margin and the actual point margin in college football bowl games?A department of transportations study on driving speed and miles per gallon for midsize automobiles resulted in the following data: Compute and interpret the sample correlation coefficient.Over the past 40 years, the percentage of homes in the United States with smoke detectors has risen steadily and has plateaued at about 96% (National Fire Protection Association website, January, 2015). With this increase in the use of home smoke detectors, what has happened to the death rate from home fires? The DATAfile SmokeDetectors contains 17 years of data on the estimated percentage of homes with smoke detectors and the estimated home fire deaths per million of population. a. Do you expect a positive or negative relationship between smoke detector use and deaths from home fires? Why or why not? b. Compute and report the correlation coefficient. is there a positive or negative correlation between smoke detector use and deaths from home fires? Comment. c. Show a scatter plot of the death rate per million of population and the percentage of homes with smoke detectors.The Russell 1000 is a stock market index consisting of the largest U.S. companies. The Dow Jones industrial Average is based on 30 large companies. The DATAfile Russell gives the annual percentage returns for each of these stock indexes for the years 1988 to 2012 (1stock1 website). a. Plot these percentage returns using a scatter plot. b. Compute the sample mean and standard deviation for each index. c. Compute the sample correlation. d. Discuss similarities and differences in these two indexes.A random sample of 30 colleges from Kiplingers list of the best values in private college provided the data shown in the DATAfile named BestPrivateColleges (Kiplinger, October 2013). The variable named Admit Rate (%) shows the percentage of students that applied to the college and were admitted, and the variable named 4-yr Grad. Rate (%) shows the percentage of students that were admitted and graduated in four years. a. Develop a scatter diagram with Admit Rate (%) as the independent variable. What does the scatter diagram indicate about the relationship between the two variables? b. Compute the sample correlation coefficient. What does the value of the sample correlation coefficient indicate about the relationship between the Admit Rate (%) and the 4-yr Grad. Rate (%)?The average number of times Americans dine out in a week fell from 4.0 in 2008 to 3.8 in 2012 (Zagat.com, April, 2012). The number of times a sample of 20 families dined out last week provides the following data. a. Compute the mean and median. b. Compute the first and third quartiles. c. Compute the range and interquartile range. d. Compute the variance and standard deviation. e. The skewness measure for these data is 0.34. Comment on the shape of this distribution. Is it the shape you would expect? Why or why not? f. Do the data contain outliers?USA Today reports that NCAA colleges and universities are paying higher salaries to a newly recruited football coach compared to what they paid their previous football coach. (USA Today, February 12, 2013). The annual base salaries for the previous head football coach and the new head football coach at 23 schools are given in the DATAfile Coaches. a. Determine the median annual salary for a previous head football coach and a new head football coach. b. Compute the range for salaries for both previous and new head football coaches. c. Compute the standard deviation for salaries for both previous and new head football coaches. d. Based on your answers to (a) to (c), comment on any differences between the annual base salary a school pays a new head football coach compared to what it paid its previous head football coach.The average waiting time for a patient at an El Paso physicians office is just over 29 minutes, well above the national average of 21 minutes. In fact, El Paso has the longest physicians office waiting times in the United States (El Paso Times, January 8, 2012). In order to address the issue of long patient wait times, some physicians offices are using wait tracking systems to notify patients of expected wait times. Patients can adjust their arrival times based on this information and spend less time in waiting rooms. The following data show wait times (minutes) for a sample of patients at offices that do not have an office tracking system and wait times for a sample of patients at offices with an office tracking system. Without Wait Tracking System With Wait Tracking System 24 31 67 11 17 14 20 18 31 12 44 37 12 9 23 13 16 12 37 15 a. What are the mean and median patient wait times for offices with a wait tracking system? What are the mean and median patient wait times for offices without a wait tracking system? b. What are the variance and standard deviation of patient wait times for offices with a wait tracking system? What are the variance and standard deviation of patient wait times for visits to offices without a wait tracking system? c. Do offices with a wait tracking system have shorter patient wait times than offices without a wait tracking system? Explain. d. Considering only offices without a wait tracking system, what is the z-score for the tenth patient in the sample? e. Considering only offices with a wait tracking system, what is the z-score for the sixth patient in the sample? How does this z-score compare with the z-score you calculated for part (d)? f. Based on z-scores, do the data for offices without a wait tracking system contain any outliers? Based on z-scores, do the data for offices with a wait tracking system contain any outliers?U.S. companies lose 63.2 billion per year from workers with insomnia. Workers lose an average of 7.8 days of productivity per year due to lack of sleep (Wall Street Journal, January 23, 2013). The following data show the number of hours of sleep attained during a recent night for a sample of 20 workers. a. What is the mean number of hours of sleep for this sample? b. What is the variance? Standard deviation?A study of smartphone users shows that 68% of smartphone use occurs at home and a user spends an average of 410 minutes per month using a smartphone to interact with other people (Harvard Business Review, JanuaryFebruary 2013). Consider the following data indicating the number of minutes in a month spent interacting with others via a smartphone for a sample of 50 smartphone users. a. What is the mean number of minutes spent interacting with others for this sample? How does it compare to the mean reported in the study? b. What is the standard deviation for this sample? c. Are there any outliers in this sample?Public transportation and the automobile are two methods an employee can use to get to work each day. Samples of times recorded for each method are shown. Times are in minutes. a. Compute the sample mean time to get to work for each method. b. Compute the sample standard deviation for each method. c. On the basis of your results from parts (a) and (b), which method of transportation should be preferred? Explain. d. Develop a box plot for each method. Does a comparison of the box plots support your conclusion in part (c)?In 2007 the New York Times reported that the median annual household income in the United States was 55,500 (New York Times website, August, 21, 2013). Answer the following questions based on the following sample of 14 household incomes for 2013 (1000s). a. What is the median household income for the sample data for 2013? b. Based on the sample data, estimate the percentage change in the median household income from 2007 to 2013. c. Compute the first and third quartiles. d. Provide a five-number summary. e. Using the z-score approach, do the data contain any outliers? Does the approach that uses the values of the first and third quartiles and the interquartile range to detect outliers provide the same results?The data contained in the DATAfile named FoodIndustry show the company/chain name, the average sales per store (1000s), and the food segment industry for 47 restaurant chains (Quick Service Restaurant Magazine website, August 2013). a. What was the mean U.S. sales per store for the 47 restaurant chains? b. What are the first and third quartiles? What is your interpretation of the quartiles? c. Show a box plot for the level of sales and discuss if there are any outliers in terms of sales that would skew the results. d. Develop a frequency distribution showing the average sales per store for each segment. Comment on the results obtained.Travel + Leisure magazine provides an annual list of the 500 best hotels in the world. The magazine provides a rating for each hotel along with a brief description that includes the size of the hotel, amenities, and the cost per night for a double room. A sample of 12 of the top-rated hotels in the United States follows. a. What is the mean number of rooms? b. What is the mean cost per night for a double room? c. Develop a scatter diagram with the number of rooms on the horizontal axis and the cost per night on the vertical axis. Does there appear to be a relationship between the number of rooms and the cost per night? Discuss. d. What is the sample correlation coefficient? What does it tell you about the relationship between the number of rooms and the cost per night for a double room? Does this appear reasonable? Discuss.The 32 teams in the National Football League (NFL) are worth, on average, 1.17 billion, 5% more than last year. The following data show the annual revenue ( millions) and the estimated team value ( millions) for the 32 NFL teams (Forbes website, February 28, 2014). a. Develop a scatter diagram with Revenue on the horizontal axis and Value on the vertical axis. Does there appear that there is any relationship between the two variables? b. What is the sample correlation coefficient? What can you say about the strength of the relationship between Revenue and Value?Does a major league baseball teams record during spring training indicate how the team will play during the regular season? Over a six-year period, the correlation coefficient between a teams winning percentage in spring training and its winning percentage in the regular season is .18. Shown are the winning percentages for the 14 American League teams during a previous season. a. What is the correlation coefficient between the spring training and the regular season winning percentages? b. What is your conclusion about a teams record during spring training indicating how the team will play during the regular season? What are some of the reasons why this occurs? Discuss.The days to maturity for a sample of five money market funds are shown here. The dollar amounts invested in the funds are provided. Use the weighted mean to determine the mean number of days to maturity for dollars invested in these five money market funds. Days to Maturity Dollar Value (millions) 20 20 12 30 7 10 5 15 6 10 Automobiles traveling on a road with a posted speed limit of 55 miles per hour are checked for speed by a state police radar system. Following is a frequency distribution of speeds. Speed (miles per hour) Frequency 4549 10 5054 40 5559 150 6064 175 6569 75 7074 15 7579 10 Total 475 a. What is the mean speed of the automobiles traveling on this road? b. Compute the variance and the standard deviation.The Panama Railroad Company was established in 1850 to construct a railroad across the isthmus that would allow fast and easy access between the Atlantic and Pacific Oceans. The following table (The Big Ditch, Mauer and Yu, 2011) provides annual returns for Panama Railroad stock from 1853 through 1880. Year Return on Panama Railroad Company Stock (%) 1853 1 1854 9 1855 19 1856 2 1857 3 1858 36 1859 21 1860 16 1861 5 1862 43 1863 44 1864 48 1865 7 1866 11 1867 23 1868 20 1869 11 1870 51 1871 42 1872 39 1873 42 1874 12 1875 26 1876 9 1877 6 1878 25 1879 31 1880 30 a. Create a graph of the annual returns on the stock. The New York Stock Exchange earned an annual average return of 8.4% from 1853 through 1880. Can you tell from the graph if the Panama Railroad Company stock outperformed the New York Stock Exchange? b. Calculate the mean annual return on Panama Railroad Company stock from 1853 through 1880. Did the stock outperform the New York Stock Exchange over the same period?Pelican Stores Pelican Stores, a division of National Clothing, is a chain of womens apparel stores operating throughout the country. The chain recently ran a promotion in which discount coupons were sent to customers of other National Clothing stores. Data collected for a sample of 100 instore credit card transactions at Pelican Stores during one day while the promotion was running are contained in the file named PelicanStores. Table 3.9 shows a portion of the data set. The proprietary card method of payment refers to charges made using a National Clothing charge card. Customers who made a purchase using a discount coupon are referred to as promotional customers and customers who made a purchase but did not use a discount coupon are referred to as regular customers. Because the promotional coupons were not sent to regular Pelican Stores customers, management considers the sales made to people presenting the promotional coupons as sales it would not otherwise make. Of course, Pelican also hopes that the promotional customers will continue to shop at its stores. TABLE 3.9 SAMPLE OF 100 CREDIT CARD PURCHASES AT PELICAN STORES Most of the variables shown in Table 3.9 are self-explanatory, but two of the variables require some clarification. Items The total number of items purchased Net Sales The total amount () charged to the credit card Pelicans management would like to use this sample data to learn about its customer base and to evaluate the promotion involving discount coupons. Managerial Report Use the methods of descriptive statistics presented in this chapter to summarize the data and comment on your findings. At a minimum, your report should include the following: 1. Descriptive statistics on net sales and descriptive statistics on net sales by various classifications of customers. 2. Descriptive statistics concerning the relationship between age and net sales.Motion Picture Industry The motion picture industry is a competitive business. More than 50 studios produce several hundred new motion pictures each year, and the financial success of the motion pictures varies considerably. The opening weekend gross sales, the total gross sales, the number of theaters the movie was shown in, and the number of weeks the motion picture was in release are common variables used to measure the success of a motion picture. Data on the top 100 grossing motion pictures released in 2011 (Box Office Mojo website, March 17, 2012) are contained in a file named 2011Movies. Table 3.10 shows the data for the first 10 motion pictures in this file. Note that some movies, such as War Horse, were released late in 2011 and continued to run in 2012. TABLE 3.10 PERFORMANCE DATA FOR 10 MOTION PICTURES Managerial Report Use the numerical methods of descriptive statistics presented in this chapter to learn how these variables contribute to the success of a motion picture. Include the following in your report: 1. Descriptive statistics for each of the four variables along with a discussion of what the descriptive statistics tell us about the motion picture industry. 2. What motion pictures, if any, should be considered high-performance outliers? Explain. 3. Descriptive statistics showing the relationship between total gross sales and each of the other variables. Discuss.Business Schools of Asia-Pacific The pursuit of a higher education degree in business is now international. A survey shows that more and more Asians choose the master of business administration (MBA) degree route to corporate success. As a result, the number of applicants for MBA courses at Asia- Pacific schools continues to increase. Across the region, thousands of Asians show an increasing willingness to temporarily shelve their careers and spend two years in pursuit of a theoretical business qualification. Courses in these schools are notoriously tough and include economics, banking, marketing, behavioral sciences, labor relations, decision making, strategic thinking, business law, and more. The data set in Table 3.11 shows some of the characteristics of the leading Asia- Pacific business schools. Managerial Report Use the methods of descriptive statistics to summarize the data in Table 3.11. Discuss your findings. 1. Include a summary for each variable in the data set. Make comments and interpretations based on maximums and minimums, as well as the appropriate means and proportions. What new insights do these descriptive statistics provide concerning Asia-Pacific business schools? 2. Summarize the data to compare the following: a. Any difference between local and foreign tuition costs. b. Any difference between mean starting salaries for schools requiring and not requiring work experience. c. Any difference between starting salaries for schools requiring and not requiring English tests. 3. Do starting salaries appear to be related to tuition? 4. Present any additional graphical and numerical summaries that will be beneficial in communicating the data in Table 3.11 to others. TABLE 3.11 DATA FOR 25 ASIA-PACIFIC BUSINESS SCHOOLS African Elephant Populations Although millions of elephants once roamed across Africa, by the mid-1980s elephant populations in African nations had been devastated by poaching. Elephants are important to African ecosystems. In tropical forests, elephants create clearings in the canopy that encourage new tree growth. In savannas, elephants reduce bush cover to create an environment that is favorable to browsing and grazing animals. In addition, the seeds of many plant species depend on passing through an elephants digestive tract before germination. The status of the elephant now varies greatly across the continent. In some nations, strong measures have been taken to effectively protect elephant populations; for example, Kenya has destroyed over five tons of elephant ivory confiscated from poachers in an attempt to deter the growth of illegal ivory trade (Associated Press, July 20, 2011). In other nations the elephant populations remain in danger due to poaching for meat and ivory, loss of habitat, and conflict with humans. Table 3.13 shows elephant populations for several African nations in 1979, 1989, and 2007 (ElephantDatabase.org website, December 15, 2014). The David Sheldrick Wildlife Trust was established in 1977 to honor the memory of naturalist David Leslie William Sheldrick, who founded Warden of Tsavo East National Park in Kenya and headed the Planning Unit of the Wildlife Conservation and Management Department in that country. Management of the Sheldrick Trust would like to know what these data indicate about elephant populations in various African countries since 1979. Managerial Report Use methods of descriptive statistics to summarize the data and comment on changes in elephant populations in African nations since 1979. At a minimum your report should include the following. 1. The mean annual change in elephant population for each country in the 10 years from 1979 to 1989, and a discussion of which countries saw the largest changes in elephant population over this 10-year period. 2. The mean annual change in elephant population for each country from 1989 to 2007, and a discussion of which countries saw the largest changes in elephant population over this 18-year period. 3. The mean annual change in elephant population for each country from 2007 to 2012, and a discussion of which countries saw the largest changes in elephant population over this 5-year period. 4. A comparison of your results from parts 1, 2, and 3, and a discussion of the conclusions you can draw from this comparison. TABLE 3.13 ELEPHANT POPULATIONS FOR SEVERAL AFRICAN NATIONS IN 1979, 1989, AND 2007 An experiment has three steps with three outcomes possible for the first step, two outcomes possible for the second step, and four outcomes possible for the third step. How many experimental outcomes exist for the entire experiment?How many ways can three items be selected from a group of six items? Use the letters A, b, C, D, E, and F to identify the items, and list each of the different combinations of three items.How many permutations of three items can be selected from a group of six? Use the letters A, b, C, D, E, and F to identify the items, and list each of the permutations of items b, D, and F.Consider the experiment of tossing a coin three times. a. Develop a tree diagram for the experiment. b. List the experimental outcomes. c. What is the probability for each experimental outcome?Suppose an experiment has five equally likely outcomes: E1, E2, E3, E4, E5. Assign probabilities to each outcome and show that the requirements in equations (4.3) and (4.4) are satisfied. What method did you use?An experiment with three outcomes has been repeated 50 times, and it was learned that E1 occurred 20 times, E2 occurred 13 times, and E3 occurred 17 times. Assign probabilities to the outcomes. What method did you use?A decision maker subjectively assigned the following probabilities to the four outcomes of an experiment: P(E1) = .10, P(E2) = .15, P(E3) = .40, and P(E4) = .20. Are these probability assignments valid? Explain.In the city of Milford, applications for zoning changes go through a two-step process: a review by the planning commission and a final decision by the city council. At step 1 the planning commission reviews the zoning change request and makes a positive or negative recommendation concerning the change. At step 2 the city council reviews the planning commissions recommendation and then votes to approve or to disapprove the zoning change. Suppose the developer of an apartment complex submits an application for a zoning change. Consider the application process as an experiment. a. How many sample points are there for this experiment? List the sample points. b. Construct a tree diagram for the experiment.Simple random sampling uses a sample of size n from a population of size N to obtain data that can be used to make inferences about the characteristics of a population. Suppose that, from a population of 50 bank accounts, we want to take a random sample of four accounts in order to learn about the population. How many different random samples of four accounts are possible?The following table shows the percentage of on-time arrivals, the number of mishandled baggage reports per 1000 passengers, and the number of customer complaints per 1000 passengers for 10 airlines (Forbes website, February, 2014). a. If you randomly choose a Delta Air Lines flight, what is the probability that this individual flight has an on-time arrival? b. If you randomly choose one of the 10 airlines for a follow-up study on airline quality ratings, what is the probability that you will choose an airline with less than two mishandled baggage reports per 1000 passengers? c. If you randomly choose 1 of the 10 airlines for a follow-up study on airline quality ratings, what is the probability that you will choose an airline with more than one customer complaint per 1000 passengers? d. What is the probability that a randomly selected AirTran Airways flight will not arrive on time?The National Occupant Protection Use Survey (NOPUS) was conducted to provide probability-based data on motorcycle helmet use in the United States. The survey was conducted by sending observers to randomly selected roadway sites where they collected data on motorcycle helmet use, including the number of motorcyclists wearing a Department of Transportation (DOT)-compliant helmet (National Highway Traffic Safety Administration website, January 7, 2010). Sample data consistent with the most recent NOPUS are shown below. a. Use the sample data to compute an estimate of the probability that a motorcyclist wears a DOT-compliant helmet. b. The probability that a motorcyclist wore a DOT-compliant helmet five years ago was .48, and last year this probability was .63. Would the National Highway Traffic Safety Administration be pleased with the most recent survey results? c. What is the probability of DOT-compliant helmet use by region of the country? What region has the highest probability of DOT-compliant helmet use?The Powerball lottery is played twice each week in 31 states, the District of Columbia, and the Virgin Islands. To play Powerball, a participant must purchase a 2 ticket, select five numbers from the digits 1 through 59, and then select a Powerball number from the digits 1 through 35. To determine the winning numbers for each game, lottery officials draw 5 white balls out a drum of 59 white balls numbered 1 through 59 and 1 red ball out of a drum of 35 red balls numbered 1 through 35. To win the Powerball jackpot, a participants numbers must match the numbers on the 5 white balls in any order and must also match the number on the red Powerball. The numbers 516222329 with a Powerball number of 6 provided the record jackpot of 580 million (Powerball website, November 29, 2012). a. How many Powerball lottery outcomes are possible? (Hint: Consider this a two-step random experiment. Select the 5 white ball numbers and then select the 1 red Powerball number.) b. What is the probability that a 2 lottery ticket wins the Powerball lottery?A company that manufactures toothpaste is studying five different package designs. Assuming that one design is just as likely to be selected by a consumer as any other design, what selection probability would you assign to each of the package designs? In an actual experiment, 100 consumers were asked to pick the design they preferred. The following data were obtained. Do the data confirm the belief that one design is just as likely to be selected as another? Explain. Design Number of Times Preferred 1 5 2 15 3 30 4 40 5 10 An experiment has four equally likely outcomes: E1, E2, E3, and E4. a. What is the probability that E2 occurs? b. What is the probability that any two of the outcomes occur (e.g., E1 or E3)? c. What is the probability that any three of the outcomes occur (e.g., E1 or E2 or E4)?Consider the experiment of selecting a playing card from a deck of 52 playing cards. Each card corresponds to a sample point with a 1/52 probability. a. List the sample points in the event an ace is selected. b. List the sample points in the event a club is selected. c. List the sample points in the event a face card (jack, queen, or king) is selected. d. Find the probabilities associated with each of the events in parts (a), (b), and (c).Consider the experiment of rolling a pair of dice. Suppose that we are interested in the sum of the face values showing on the dice. a. How many sample points are possible? (Hint: use the counting rule for multiple-step experiments.) b. List the sample points. c. What is the probability of obtaining a value of 7? d. What is the probability of obtaining a value of 9 or greater? e. Because each roll has six possible even values (2, 4, 6, 8, 10, and 12) and only five possible odd values (3, 5, 7, 9, and 11), the dice should show even values more often than odd values. Do you agree with this statement? Explain. f. What method did you use to assign the probabilities requested?Refer to the KPL sample points and sample point probabilities in Tables 4.2 and 4.3. a. The design stage (stage 1) will run over budget if it takes 4 months to complete. List the sample points in the event the design stage is over budget. b. What is the probability that the design stage is over budget? c. The construction stage (stage 2) will run over budget if it takes 8 months to complete. List the sample points in the event the construction stage is over budget. d. What is the probability that the construction stage is over budget? e. What is the probability that both stages are over budget?Fortune magazine publishes an annual list of the 500 largest companies in the United States. The corporate headquarters for the 500 companies are located in 38 different states. The following table shows the 8 states with the largest number of Fortune 500 companies (Money/CNN website, May, 2012). Suppose one of the 500 companies is selected at random for a follow-up questionnaire. a. What is the probability that the company selected has its corporate headquarters in California? b. What is the probability that the company selected has its corporate headquarters in California, New York, or Texas? c. What is the probability that the company selected has its corporate headquarters in one of the 8 states listed above?Do you think global warming will have an impact on you during your lifetime? A CBS News/New York times poll of 1000 adults in the United States asked this question (CBS News website, December, 2014). Consider the responses by age groups shown below. a. What is the probability that a respondent 1829 years of age thinks that global warming will not pose a serious threat during his/her lifetime? b. What is the probability that a respondent 30+ years of age thinks that global warming will not pose a serious threat during his/her lifetime? c. For a randomly selected respondent, what is the probability that a respondent answers yes? d. Based on the survey results, does there appear to be a difference between ages 1829 and 30+ regarding concern over global warming?Junior Achievement USA and the Allstate Foundation surveyed teenagers aged 14 to 18 and asked at what age they think that they will become financially independent (USA Today, April 30, 2012). The responses of 944 teenagers who answered this survey question are as follows. Age Financially Independent Number of Responses 16 to 20 191 21 to 24 467 25 to 27 244 28 or older 42 Consider the experiment of randomly selecting a teenager from the population of teenagers aged 14 to 18. a. Compute the probability of being financially independent for each of the four age categories. b. What is the probability of being financially independent before the age of 25? c. What is the probability of being financially independent after the age of 24? d. Do the probabilities suggest that the teenagers may be somewhat unrealistic in their expectations about when they will become financially independent?Data on U.S. work-related fatalities by cause follow (The World Almanac, 2012). Cause of Fatality Number of Fatalities Transportation incidents 1795 Assaults and violent acts 837 Contact with objects and equipment 741 Falls 645 Exposure to harmful substances or environments 404 Fires and explosions 113 Assume that a fatality will be randomly chosen from this population. a. What is the probability the fatality resulted from a fall? b. What is the probability the fatality resulted from a transportation incident? c. What cause of fatality is least likely to occur? What is the probability the fatality resulted from this cause?Suppose that we have a sample space with five equally likely experimental outcomes: E1, E2, E3, E4, E5. Let A = {E1, E2} B = {E3, E4} C = {E2, E3, E5} a. Find P(A), P(B), and P(C). b. Find P(A B). Are A and B mutually exclusive? c. Find Ac, Cc, P(Ac), and P(Cc). d. Find A Bc and P(A Bc). e. Find P(B C).Suppose that we have a sample space S = {E1, E2, E3, E4, E5, E6, E7}, where E1, E2, , E7 denote the sample points. The following probability assignments apply: P(E1) = .05, P(E2) = .20, P(E3) = .20, P(E4) = .25, P(E5) = .15, P(E6) = .10, and P(E7) = .05. Let A = {E1, E4, E6} B = {E2, E4, E7} C = {E2, E3, E5, E7} a. Find P(A), P(B), and P(C). b. Find A B and P(A B). c. Find A B and P(A B). d. Are events A and C mutually exclusive? e. Find Bc and P(Bc).Clarkson University surveyed alumni to learn more about what they think of Clarkson. One part of the survey asked respondents to indicate whether their overall experience at Clarkson fell short of expectations, met expectations, or surpassed expectations. The results showed that 4% of the respondents did not provide a response, 26% said that their experience fell short of expectations, and 65% of the respondents said that their experience met expectations. a. If we chose an alumnus at random, what is the probability that the alumnus would say their experience surpassed expectations? b. If we chose an alumnus at random, what is the probability that the alumnus would say their experience met or surpassed expectations?The Eco Pulse survey from the marketing communications firm Shelton Group asked individuals to indicate things they do that make them feel guilty (Los Angeles Times, August 15, 2012). Based on the survey results, there is a .39 probability that a randomly selected person will feel guilty about wasting food and a .27 probability that a randomly selected person will feel guilty about leaving lights on when not in a room. Moreover, there is a .12 probability that a randomly selected person will feel guilty for both of these reasons. a. What is the probability that a randomly selected person will feel guilty for either wasting food or leaving lights on when not in a room? b. What is the probability that a randomly selected person will not feel guilty for either of these reasons?Information about mutual funds provided by Morningstar includes the type of mutual fund (Domestic Equity, International Equity, or Fixed Income) and the Morningstar rating for the fund. The rating is expressed from 1-star (lowest rating) to 5-star (highest rating). Suppose a sample of 25 mutual funds provided the following counts: Sixteen mutual funds were Domestic Equity funds. Thirteen mutual funds were rated 3-star or less. Seven of the Domestic Equity funds were rated 4-star. Two of the Domestic Equity funds were rated 5-star. Assume that one of these 25 mutual funds will be randomly selected in order to learn more about the mutual fund and its investment strategy. a. What is the probability of selecting a Domestic Equity fund? b. What is the probability of selecting a fund with a 4-star or 5-star rating? c. What is the probability of selecting a fund that is both a Domestic Equity fund and a fund with a 4-star or 5-star rating? d. What is the probability of selecting a fund that is a Domestic Equity fund or a fund with a 4-star or 5-star rating?What NCAA college basketball conferences have the higher probability of having a team play in college basketballs national championship game? Over the last 20 years, the Atlantic Coast Conference (ACC) ranks first by having a team in the championship game 10 times. The Southeastern Conference (SEC) ranks second by having a team in the championship game 8 times. However, these two conferences have both had teams in the championship game only one time, when Arkansas (SEC) beat Duke (ACC) 7670 in 1994 (NCAA website, April 2009). Use these data to estimate the following probabilities. a. What is the probability the ACC will have a team in the championship game? b. What is the probability the SEC will have team in the championship game? c. What is the probability the ACC and SEC will both have teams in the championship game? d. What is the probability at least one team from these two conferences will be in the championship game? That is, what is the probability a team from the ACC or SEC will play in the championship game? e. What is the probability that the championship game will not a have team from one of these two conferences?A survey of magazine subscribers showed that 45.8% rented a car during the past 12 months for business reasons, 54% rented a car during the past 12 months for personal reasons, and 30% rented a car during the past 12 months for both business and personal reasons. a. What is the probability that a subscriber rented a car during the past 12 months for business or personal reasons? b. What is the probability that a subscriber did not rent a car during the past 12 months for either business or personal reasons?High school seniors with strong academic records apply to the nations most selective colleges in greater numbers each year. Because the number of slots remains relatively stable, some colleges reject more early applicants. Suppose that for a recent admissions class, an Ivy League college received 2851 applications for early admission. Of this group, it admitted 1033 students early, rejected 854 outright, and deferred 964 to the regular admission pool for further consideration. In the past, this school has admitted 18% of the deferred early admission applicants during the regular admission process. Counting the students admitted early and the students admitted during the regular admission process, the total class size was 2375. Let E, R, and D represent the events that a student who applies for early admission is admitted early, rejected outright, or deferred to the regular admissions pool. a. Use the data to estimate P(E), P(R), and P(D). b. Are events E and D mutually exclusive? Find P(E D). c. For the 2375 students who were admitted, what is the probability that a randomly selected student was accepted during early admission? d. Suppose a student applies for early admission. What is the probability that the student will be admitted for early admission or be deferred and later admitted during the regular admission process?Suppose that we have two events, A and B, with P(A) = .50, P(B) = .60, and P(A B) = .40. a. Find P(A B). b. Find P(B A). c. Are A and B independent? Why or why not?Assume that we have two events, A and B, that are mutually exclusive. Assume further that we know P(A) = .30 and P(B) = .40. a. What is P(A B)? b. What is P(A B)? c. A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent. Do you agree with this statement? Use the probability information in this problem to justify your answer. d. What general conclusion would you make about mutually exclusive and independent events given the results of this problem?The automobile industry sold 657,000 vehicles in the United States during January 2009 (The Wall Street Journal, February 4, 2009). This volume was down 37% from January 2008 as economic conditions continued to decline. The big Three U.S. automakersGeneral Motors, Ford, and Chryslersold 280,500 vehicles, down 48% from January 2008. A summary of sales by automobile manufacturer and type of vehicle sold is shown in the following table. Data are in thousands of vehicles. The non-U.S. manufacturers are led by Toyota, Honda, and Nissan. The category light Truck includes pickup, minivan, SUV, and crossover models. a. Develop a joint probability table for these data and use the table to answer the remaining questions. b. What are the marginal probabilities? What do they tell you about the probabilities associated with the manufacturer and the type of vehicle sold? c. If a vehicle was manufactured by one of the U.S. automakers, what is the probability that the vehicle was a car? What is the probability it was a light truck? d. If a vehicle was not manufactured by one of the U.S. automakers, what is the probability that the vehicle was a car? What is the probability it was a light truck? e. If the vehicle was a light truck, what is the probability that it was manufactured by one of the U.S. automakers? f. What does the probability information tell you about sales?Students taking the Graduate Management Admissions Test (GMAT) were asked about their undergraduate major and intent to pursue their MBA as a full-time or part-time student. A summary of their responses follows. a. Develop a joint probability table for these data. b. Use the marginal probabilities of undergraduate major (business, engineering, or other) to comment on which undergraduate major produces the most potential MBA students. c. If a student intends to attend classes full-time in pursuit of an MBA degree, what is the probability that the student was an undergraduate engineering major? d. If a student was an undergraduate business major, what is the probability that the student intends to attend classes full-time in pursuit of an MBA degree? e. Let A denote the event that the student intends to attend classes full-time in pursuit of an MBA degree, and let B denote the event that the student was an undergraduate business major. Are events A and B independent? Justify your answer.The bureau of Transportation Statistics reports on-time performance for airlines at major U.S. airports. JetBlue, united, and US Airways share terminal C at Bostons Logan Airport. The percentage of on-time flights reported for August 2012 was 76.8% for JetBlue, 71.5% for United, and 82.2% for US Airways (Bureau of Transportation Statistics website, October 2012). Assume that 30% of the flights arriving at terminal C are JetBlue flights, 32% are united flights, and 38% are US Airways flights. a. Develop a joint probability table with three rows (the airlines) and two columns (on-time and late). b. An announcement is made that Flight 1382 will be arriving at gate 20 of terminal C. What is the probability that Flight 1382 will arrive on time? c. What is the most likely airline for Flight 1382? What is the probability that Flight 1382 is by this airline? d. Suppose that an announcement is made saying that Flight 1382 will now be arriving late. What is the most likely airline for this flight? What is the probability that Flight 1382 is by this airline?To better understand how husbands and wives feel about their finances, Money Magazine conducted a national poll of 1010 married adults age 25 and older with household incomes of 50,000 or more (Money Magazine website, December 14, 2014). Consider the following example set of responses to the question, Who is better at getting deals? a. Develop a joint probability table and use it to answer the following questions. b. Construct the marginal probabilities for Who Is better (I Am, My Spouse, We Are Equal). Comment. c. Given that the respondent is a husband, what is the probability that he feels he is better at getting deals than his wife? d. Given that the respondent is a wife, what is the probability that she feels she is better at getting deals than her husband? e. Given a response My spouse is better at getting deals, what is the probability that the response came from a husband? f. Given a response We are equal, what is the probability that the response came from a husband? What is the probability that the response came from a wife?Jamal Crawford of the National Basketball Associations Portland Trail Blazers is the best free-throw shooter on the team, making 93% of his shots (ESPN website, April 5, 2012). Assume that late in a basketball game, Jamal Crawford is fouled and is awarded two shots. a. What is the probability that he will make both shots? b. What is the probability that he will make at least one shot? c. What is the probability that he will miss both shots? d. Late in a basketball game, a team often intentionally fouls an opposing player in order to stop the game clock. The usual strategy is to intentionally foul the other teams worst free-throw shooter. Assume that the Portland Trail Blazers center makes 58% of his free-throw shots. Calculate the probabilities for the center as shown in parts (a), (b), and (c), and show that intentionally fouling the Portland Trail Blazers center is a better strategy than intentionally fouling Jamal Crawford. Assume as in parts (a), (b), and (c) that two shots will be awarded.A joint survey by Parade magazine and Yahoo! found that 59% of American workers say that if they could do it all over again, they would choose a different career (USA Today, September 24, 2012). The survey also found that 33% of American workers say they plan to retire early and 67% say they plan to wait and retire at age 65 or older. Assume that the following joint probability table applies. a. What is the probability a worker would select the same career? b. What is the probability a worker who would select the same career plans to retire early? c. What is the probability a worker who would select a different career plans to retire early? d. What do the conditional probabilities in parts (b) and (c) suggest about the reasons workers say they would select the same career?The Institute for Higher Education Policy, a Washington, D.C.-based research firm, studied the payback of student loans for 1.8 million college students who had student loans that began to become due six years ago (The Wall Street Journal, November 27, 2012). The study found that 50% of the student loans were being paid back in a satisfactory fashion, whereas 50% of the student loans were delinquent. The following joint probability table shows the probabilities of the student loan status and whether or not the student had received a college degree. a. What is the probability that a student with a student loan had received a college degree? b. What is the probability that a student with a student loan had not received a college degree? c. Given the student had received a college degree, what is the probability that the student has a delinquent loan? d. Given the student had not received a college degree, what is the probability that the student has a delinquent loan? e. What is the impact of dropping out of college without a degree for students who have a student loan?The prior probabilities for events A1 and A2 are P(A1) = .40 and P(A2) = .60. It is also known that P(A1 A2) = 0. Suppose P(B A1) = .20 and P(B A2) = .05. a. Are A1 and A2 mutually exclusive? Explain. b. Compute P(A1 B) and P(A2 B). c. Compute P(B). d. Apply Bayes theorem to compute P(A1 B) and P(A2 B).The prior probabilities for events A1, A2, and A3 are P(A1) = .20, P(A2) = .50, and P(A3) = .30. The conditional probabilities of event B given A1, A2, and A3 are P(B A1) = .50, P(B A2) = .40, and P(B A3) = .30. a. Compute P(B A1), P(B A2), and P(B A3). b. Apply Bayes theorem, equation (4.19), to compute the posterior probability P(A2 B). c. Use the tabular approach to applying Bayes theorem to compute P(A1 B), P(A2 B), and P(A3 B).A consulting firm submitted a bid for a large research project. The firms management initially felt they had a 5050 chance of getting the project. However, the agency to which the bid was submitted subsequently requested additional information on the bid. Past experience indicates that for 75% of the successful bids and 40% of the unsuccessful bids the agency requested additional information. a. What is the prior probability of the bid being successful (that is, prior to the request for additional information)? b. What is the conditional probability of a request for additional information given that the bid will ultimately be successful? c. Compute the posterior probability that the bid will be successful given a request for additional information.A local bank reviewed its credit card policy with the intention of recalling some of its credit cards. In the past approximately 5% of cardholders defaulted, leaving the bank unable to collect the outstanding balance. Hence, management established a prior probability of .05 that any particular cardholder will default. The bank also found that the probability of missing a monthly payment is .20 for customers who do not default. Of course, the probability of missing a monthly payment for those who default is 1. a. Given that a customer missed one or more monthly payments, compute the posterior probability that the customer will default. b. The bank would like to recall its card if the probability that a customer will default is greater than .20. Should the bank recall its card if the customer misses a monthly payment? Why or why not?In August 2012, tropical storm Isaac formed in the Caribbean and was headed for the Gulf of Mexico. There was an initial probability of .69 that Isaac would become a hurricane by the time it reached the Gulf of Mexico (National Hurricane Center website, August 21, 2012). a. What was the probability that Isaac would not become a hurricane but remain a tropical storm when it reached the Gulf of Mexico? b. Two days later, the National Hurricane Center projected the path of Isaac would pass directly over Cuba before reaching the Gulf of Mexico. How did passing over Cuba alter the probability that Isaac would become a hurricane by the time it reached the Gulf of Mexico? Use the following probabilities to answer this question. Hurricanes that reach the Gulf of Mexico have a .08 probability of having passed over Cuba. Tropical storms that reach the Gulf of Mexico have a .20 probability of having passed over Cuba. c. What happens to the probability of becoming a hurricane when a tropical storm passes over a landmass such as Cuba?ParFore created a website to market golf equipment and golf apparel. Management would like a special pop-up offer to appear for female website visitors and a different special pop-up offer to appear for male website visitors. From a sample of past website visitors, ParFores management learned that 60% of the visitors are male and 40% are female. a. What is the probability that a current visitor to the website is female? b. Suppose 30% of ParFores female visitors previously visited the Dillards Department Store website and 10% of ParFores male visitors previously visited the Dillards Department Store website. If the current visitor to ParFores website previously visited the Dillards website, what is the revised probability that the current visitor is female? Should the ParFores website display the special offer that appeals to female visitors or the special offer that appeals to male visitors?The percentage of adult users of the Internet who use Facebook has increased over time (Pew Research Internet Project, 2013). Of adult Internet users age 1849, 81% use Facebook. Of adult Internet users age 50 and older, 54% use Facebook. Assume that 52% of adult Internet users are age 1849. a. What is the probability that a randomly selected adult user of the Internet is age 50 or older? b. Given that an adult Internet user uses Facebook, what is the probability that he/she is age 1849?A survey of adults aged 18 and older conducted by Princess Cruises asked how many days into your vacation does it take until you feel truly relaxed (USA Today, August 24, 2011). The responses were as follows: 422a day or less; 1812 days; 803 days; 1214 or more days; and 201never feel relaxed. a. How many adults participated in the Princess Cruises survey? b. What response has the highest probability? What is the probability of this response? c. What is the probability a respondent never feels truly relaxed on a vacation? d. What is the probability it takes a respondent 2 or more days to feel truly relaxed?A financial manager made two new investmentsone in the oil industry and one in municipal bonds. After a one-year period, each of the investments will be classified as either successful or unsuccessful. Consider the making of the two investments as a random experiment. a. How many sample points exist for this experiment? b. Show a tree diagram and list the sample points. c. Let O = the event that the oil industry investment is successful and M = the event that the municipal bond investment is successful. List the sample points in O and in M. d. List the sample points in the union of the events (O M). e. List the sample points in the intersection of the events (O M). f. Are events O and M mutually exclusive? Explain.Forty-three percent of Americans use social media and other websites to voice their opinions about television programs (The Huffington Post, November 23, 2011). Below are the results of a survey of 1400 individuals who were asked if they use social media and other websites to voice their opinions about television programs. Uses Social Media and Other Websites to Voice Opinions About Television Programs Doesnt Use Social Media and Other Websites to Voice Opinions About Television Programs Female 395 291 Male 323 355 a. What is the probability a respondent is female? b. What is the conditional probability a respondent uses social media and other websites to voice opinions about television programs given the respondent is female? c. Let F denote the event that the respondent is female and A denote the event that the respondent uses social media and other websites to voice opinions about television programs. Are events F and A independent?A study of 31,000 hospital admissions in New York State found that 4% of the admissions led to treatment-caused injuries. One-seventh of these treatment-caused injuries resulted in death, and one-fourth were caused by negligence. Malpractice claims were filed in one out of 7.5 cases involving negligence, and payments were made in one out of every two claims. a. What is the probability a person admitted to the hospital will suffer a treatment-caused injury due to negligence? b. What is the probability a person admitted to the hospital will die from a treatment-caused injury? c. In the case of a negligent treatment-caused injury, what is the probability a malpractice claim will be paid?A telephone survey to determine viewer response to a new television show obtained the following data. Rating Frequency Poor 4 Below average 8 Average 11 Above average 14 Excellent 13 a. What is the probability that a randomly selected viewer will rate the new show as average or better? b. What is the probability that a randomly selected viewer will rate the new show below average or worse?The U.S. Census Bureau serves as the leading source of quantitative data about the nations people and economy. The following crosstabulation shows the number of households (1000s) and the household income by the highest level of education for the head of household (U.S. Census Bureau website, 2013). Only households in which the head has a high school diploma or more are included. a. Develop a joint probability table. b. What is the probability of the head of one of these households having a masters degree or more education? c. What is the probability of a household headed by someone with a high school diploma earning 100,000 or more? d. What is the probability of one of these households having an income below 25,000? e. What is the probability of a household headed by someone with a bachelors degree earning less than 25,000? f. Is household income independent of educational level?An MBA new-matriculants survey provided the following data for 2018 students. a. For a randomly selected MBA student, prepare a joint probability table for the experiment consisting of observing the students age and whether the student applied to one or more schools. b. What is the probability that a randomly selected applicant is 23 or under? c. What is the probability that a randomly selected applicant is older than 26? d. What is the probability that a randomly selected applicant applied to more than one school?Refer again to the data from the MBA new-matriculants survey in exercise 52. a. Given that a person applied to more than one school, what is the probability that the person is 2426 years old? b. Given that a person is in the 36-and-over age group, what is the probability that the person applied to more than one school? c. What is the probability that a person is 2426 years old or applied to more than one school? d. Suppose a person is known to have applied to only one school. What is the probability that the person is 31 or more years old? e. Is the number of schools applied to independent of age? Explain.In February 2012, the Pew Internet American Life project conducted a survey that included several questions about how Internet users feel about search engines and other websites collecting information about them and using this information either to shape search results or target advertising to them (Pew Research Center, March 9, 2012). In one question, participants were asked, If a search engine kept track of what you search for, and then used that information to personalize your future search results, how would you feel about that? Respondents could indicate either Would not be okay with it because you feel it is an invasion of your privacy or Would be okay with it, even if it means they are gathering information about you. Frequencies of responses by age group are summarized in the following table. Age Not Okay Okay 1829 .1485 .0604 3049 .2273 .0907 50+ .4008 .0723 a. What is the probability a survey respondent will say she or he is not okay with this practice? b. Given a respondent is 3049 years old, what is the probability the respondent will say she or he is okay with this practice? c. Given a respondent says she or he is not okay with this practice, what is the probability the respondent is 50+ years old? d. Is the attitude about this practice independent of the age of the respondent? Why or why not? e. Do attitudes toward this practice for respondents who are 1829 years old and respondents who are 50+ years old differ?A large consumer goods company ran a television advertisement for one of its soap products. On the basis of a survey that was conducted, probabilities were assigned to the following events. B = individual purchased the product S = individual recalls seeing the advertisement B S = individual purchased the product and recalls seeing the advertisement The probabilities assigned were P(B) = .20, P(S) = .40, and P(B S) = .12. a. What is the probability of an individuals purchasing the product given that the individual recalls seeing the advertisement? Does seeing the advertisement increase the probability that the individual will purchase the product? As a decision maker, would you recommend continuing the advertisement (assuming that the cost is reasonable)? b. Assume that individuals who do not purchase the companys soap product buy from its competitors. What would be your estimate of the companys market share? Would you expect that continuing the advertisement will increase the companys market share? Why or why not? c. The company also tested another advertisement and assigned it values of P(S) = .30 and P(B S) = .10. What is P(B S) for this other advertisement? Which advertisement seems to have had the bigger effect on customer purchases?Cooper Realty is a small real estate company located in Albany, New York, specializing primarily in residential listings. They recently became interested in determining the likelihood of one of their listings being sold within a certain number of days. An analysis of company sales of 800 homes in previous years produced the following data. a. If A is defined as the event that a home is listed for more than 90 days before being sold, estimate the probability of A. b. If B is defined as the event that the initial asking price is under 150,000, estimate the probability of B. c. What is the probability of A B? d. Assuming that a contract was just signed to list a home with an initial asking price of less than 150,000, what is the probability that the home will take Cooper Realty more than 90 days to sell? e. Are events A and B independent?A company studied the number of lost-time accidents occurring at its Brownsville, Texas, plant. Historical records show that 6% of the employees suffered lost-time accidents last year. Management believes that a special safety program will reduce such accidents to 5% during the current year. In addition, it estimates that 15% of employees who had lost-time accidents last year will experience a lost-time accident during the current year. a. What percentage of the employees will experience lost-time accidents in both years? b. What percentage of the employees will suffer at least one lost-time accident over the two-year period?According to the Open Doors Report, 9.5% of all full-time U.S. undergraduate students study abroad (Institute of International Education, November 14, 2011). Assume that 60% of the undergraduate students who study abroad are female and that 49% of the undergraduate students who do not study abroad are female. a. Given a female undergraduate student, what is the probability that she studies abroad? b. Given a male undergraduate student, what is the probability that he studies abroad? c. What is the overall percentage of full-time female undergraduate students? What is the overall percentage of full-time male undergraduate students?An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities. P(high-quality oil) = .50 P(medium-quality oil) = .20 P(no oil) = .30 a. What is the probability of finding oil? b. After 200 feet of drilling on the first well, a soil test is taken. The probabilities of finding the particular type of soil identified by the test follow. P(soil | high-quality oil) = .20 P(soil | medium-quality oil) = .80 P(soil | no oil) = .20 How should the firm interpret the soil test? What are the revised probabilities, and what is the new probability of finding oil?The five most common words appearing in spam emails are shipping!, today!, here!, available, and fingertips! (Andy Greenberg, The Most Common Words In Spam Email, Forbes website, March 17, 2010). Many spam filters separate spam from ham (email not considered to be spam) through application of Bayes theorem. Suppose that for one email account, 1 in every 10 messages is spam and the proportions of spam messages that have the five most common words in spam email are given below. shipping! .051 today! .045 here! .034 available .014 fingertips! .014 Also suppose that the proportions of ham messages that have these words are shipping! .0015 today! .0022 here! .0022 available .0041 fingertips! .0011 a. If a message includes the word shipping!, what is the probability the message is spam? If a message includes the word shipping!, what is the probability the message is ham? Should messages that include the word shipping! be flagged as spam? b. If a message includes the word today!, what is the probability the message is spam? If a message includes the word here!, what is the probability the message is spam? Which of these two words is a stronger indicator that a message is spam? Why? c. If a message includes the word available, what is the probability the message is spam? If a message includes the word fingertips!, what is the probability the message is spam? Which of these two words is a stronger indicator that a message is spam? Why? d. What insights do the results of parts (b) and (c) yield about what enables a spam filter that uses Bayes theorem to work effectively?Consider the experiment of tossing a coin twice. a. List the experimental outcomes. b. Define a random variable that represents the number of heads occurring on the twotosses. c. Show what value the random variable would assume for each of the experimentaloutcomes. d. Is this random variable discrete or continuous?Consider the experiment of a worker assembling a product. a. Define a random variable that represents the time in minutes required to assemblethe product. b. What values may the random variable assume? c. Is the random variable discrete or continuous?Three students scheduled interviews for summer employment at the Brookwood Institute.In each case the interview results in either an offer for a position or no offer. Experimentaloutcomes are defined in terms of the results of the three interviews. a. List the experimental outcomes. b. Define a random variable that represents the number of offers made. Is the randomvariable continuous? c. Show the value of the random variable for each of the experimental outcomes. d. Is this random variable discrete or continuous?In January the U.S. unemployment rate dropped to 8.3% (U.S. Department of Labor website, February 10, 2012). The Census Bureau includes nine states in the Northeast region.Assume that the random variable of interest is the number of Northeastern states with anunemployment rate in January that was less than 8.3%. What values may this random variable assume?To perform a certain type of blood analysis, lab technicians must perform two procedures.The first procedure requires either one or two separate steps, and the second procedurerequires either one, two, or three steps. a. List the experimental outcomes associated with performing the blood analysis. b. If the random variable of interest is the total number of steps required to do the complete analysis (both procedures), show what value the random variable will assumefor each of the experimental outcomes.Listed is a series of experiments and associated random variables. In each case, identifythe values that the random variable can assume and state whether the random variable isdiscrete or continuous. Experiment Random Variable (x) a. Take a 20-question examination Number of questions answered correctly b. Observe cars arriving at a tollbooth for 1 hour Number of cars arriving at tollbooth c. Audit 50 tax returns Number of returns containing errors d. Observe an employees work Number of nonproductive hours in an eight-hour workday e. Weigh a shipment of goods Number of pounds The probability distribution for the random variable x follows. x f (x) 20 .20 25 .15 30 .25 35 .40 a. Is this probability distribution valid? Explain. b. What is the probability that x = 30? c. What is the probability that x is less than or equal to 25? d. What is the probability that x is greater than 30?The following data were collected by counting the number of operating rooms in use atTampa General Hospital over a 20-day period: On three of the days only one operatingroom was used, on five of the days two were used, on eight of the days three were used,and on four days all four of the hospitals operating rooms were used. a. Use the relative frequency approach to construct an empirical discrete probabilitydistribution for the number of operating rooms in use on any given day. b. Draw a graph of the probability distribution. c. Show that your probability distribution satisfies the required conditions for a validdiscrete probability distribution.For unemployed persons in the United States, the average number of months of unemployment at the end of December 2009 was approximately seven months (Bureau of LaborStatistics, January 2010). Suppose the following data are for a particular region in upstateNew York. The values in the first column show the number of months unemployed andthe values in the second column show the corresponding number of unemployed persons. Months Unemployed Number Unemployed 1 1029 2 1686 3 2269 4 2675 5 3487 6 4652 7 4145 8 3587 9 2325 10 1120 Let x be a random variable indicating the number of months a person is unemployed. a. Use the data to develop an empirical discrete probability distribution for x. b. Show that your probability distribution satisfies the conditions for a valid discreteprobability distribution. c. What is the probability that a person is unemployed for two months or less? Unemployed for more than two months? d. What is the probability that a person is unemployed for more than six months?The percent frequency distributions of job satisfaction scores for a sample of informationsystems (IS) senior executives and middle managers are as follows. The scores range from alow of 1 (very dissatisfied) to a high of 5 (very satisfied). Job Satisfaction Score IS Senior Executives (%) IS Middle Managers (%) 1 5 4 2 9 10 3 3 12 4 42 46 5 41 28 a. Develop a probability distribution for the job satisfaction score of a senior executive. b. Develop a probability distribution for the job satisfaction score of a middle manager. c. What is the probability a senior executive will report a job satisfaction score of 4 or 5? d. What is the probability a middle manager is very satisfied? e. Compare the overall job satisfaction of senior executives and middle managers.A technician services mailing machines at companies in the Phoenix area. Depending onthe type of malfunction, the service call can take 1, 2, 3, or 4 hours. The different types ofmalfunctions occur at about the same frequency. a. Develop a probability distribution for the duration of a service call. b. Draw a graph of the probability distribution. c. Show that your probability distribution satisfies the conditions required for a discreteprobability function. d. What is the probability a service call will take three hours? e. A service call has just come in, but the type of malfunction is unknown. It is 3:00 p.m.and service technicians usually get off at 5:00 p.m. What is the probability the servicetechnician will have to work overtime to fix the machine today?Time Warner Cable provides television and Internet service to over 15 million people(Time Warner Cable website, October 24, 2012). Suppose that the management of TimeWarner Cable subjectively assesses a probability distribution for the number of new subscribers next year in the state of New York as follows. x f (x) 100,000 .10 200,000 .20 300,000 .25 400,000 .30 500,000 .10 600,000 .05 a. Is this probability distribution valid? Explain. b. What is the probability Time Warner will obtain more than 400,000 new subscribers? c. What is the probability Time Warner will obtain fewer than 200,000 new subscribers?A psychologist determined that the number of sessions required to obtain the trust ofa new patient is either 1, 2, or 3. Let x be a random variable indicating the number of sessions required to gain the patients trust. The following probability function has been proposed. f(x)=x6 for x = 1, 2, or 3 a. Is this probability function valid? Explain. b. What is the probability that it takes exactly 2 sessions to gain the patients trust? c. What is the probability that it takes at least 2 sessions to gain the patients trust?The following table is a partial probability distribution for the MRA Companys projectedprofits (x = profit in 1000s) for the first year of operation (the negative value denotes a loss). x f (x) 100 .10 0 .20 50 .30 100 .25 150 .10 200 a. What is the proper value for f(200)? What is your interpretation of this value? b. What is the probability that MRA will be profitable? c. What is the probability that MRA will make at least 100,000?The following table provides a probability distribution for the random variable x. x f (x) 3 .25 6 .50 9 .25 a. Compute E(x), the expected value of x. b. Compute 2, the variance of x. c. Compute , the standard deviation of x.The following table provides a probability distribution for the random variable y. y f (y) 2 .20 4 .30 7 .40 8 .10 a. Compute E(y). b. Compute Var(y) and .During the summer of 2014, Coldstream Country Club in Cincinnati, Ohio collected dataon 443 rounds of golf played from its white tees. The data for each golfers score on thetwelfth hole are contained in the DATAfile Coldstream12. a. Construct an empirical discrete probability distribution for the player scores on thetwelfth hole. b. A par is the score that a good golfer is expected to get for the hole. For hole number12, par is four. What is the probability of a player scoring less than or equal to par onhole number 12? c. What is the expected score for hole number 12? d. what is the variance for hole number 12? e. What is the standard deviation for hole number 12?The American Housing Survey reported the following data on the number of times thatowner-occupied and renter-occupied units had a water supply stoppage lasting 6 or morehours in the past 3 months (U.S. Census Bureau website, October 2012). Number of Units (1000s) Number of Times Owner Occupied Renter Occupied 0 439 394 1 1100 760 2 249 221 3 98 92 4 times or more 120 111 a. Define a random variable x = number of times that owner-occupied units had a watersupply stoppage lasting 6 or more hours in the past 3 months and develop a probabilitydistribution for the random variable. (Let x = 4 represent 4 or more times.) b. Compute the expected value and variance for x. c. Define a random variable y = number of times that renter-occupied units had a watersupply stoppage lasting 6 or more hours in the past 3 months and develop a probabilitydistribution for the random variable. (Let y = 4 represent 4 or more times.) d. Compute the expected value and variance for y. e. What observations can you make from a comparison of the number of water supplystoppages reported by owner-occupied units versus renter-occupied units?West Virginia has one of the highest divorce rates in the nation, with an annual rate ofapproximately 5 divorces per 1000 people (Centers for Disease Control and Preventionwebsite, January 12, 2012). The Marital Counseling Center, Inc. (MCC) thinks that thehigh divorce rate in the state may require them to hire additional staff. Working with aconsultant, the management of MCC has developed the following probability distributionfor x = the number of new clients for marriage counseling for the next year. x f(x) 10 .05 20 .10 30 .10 40 .20 50 .35 60 .20 a. Is this probability distribution valid? Explain. b. What is the probability MCC will obtain more than 30 new clients? c. What is the probability MCC will obtain fewer than 20 new clients? d. Compute the expected value and variance of x.The probability distribution for damage claims paid by the Newton Automobile InsuranceCompany on collision insurance follows. Payment () Probability 0 .85 500 .04 1000 .04 3000 .03 5000 .02 8000 .01 10000 .01 a. Use the expected collision payment to determine the collision insurance premium thatwould enable the company to break even. b. The insurance company charges an annual rate of 520 for the collision coverage.What is the expected value of the collision policy for a policyholder? (Hint: It is theexpected payments from the company minus the cost of coverage.) Why does thepolicyholder purchase a collision policy with this expected value?The following probability distributions of job satisfaction scores for a sample of informationsystems (IS) senior executives and middle managers range from a low of 1 (very dissatisfied) to a high of 5 (very satisfied). Probability Job Satisfaction Score IS Senior Executives IS Middle Managers 1 .05 .04 2 .09 .10 3 .03 .12 4 .42 .46 5 .41 .28 a. What is the expected value of the job satisfaction score for senior executives? b. What is the expected value of the job satisfaction score for middle managers? c. Compute the variance of job satisfaction scores for executives and middle managers. d. Compute the standard deviation of job satisfaction scores for both probability distributions. e. Compare the overall job satisfaction of senior executives and middle managers.The demand for a product of Carolina Industries varies greatly from month to month. Theprobability distribution in the following table, based on the past two years of data, showsthe companys monthly demand. Unit Demand Probability 300 .20 400 .30 500 .35 600 .15 a. If the company bases monthly orders on the expected value of the monthly demand,what should Carolinas monthly order quantity be for this product? b. Assume that each unit demanded generates 70 in revenue and that each unit orderedcosts 50. How much will the company gain or lose in a month if it places an orderbased on your answer to part (a) and the actual demand for the item is 300 units?In Gallups Annual Consumption Habits Poll, telephone interviews were conducted for arandom sample of 1014 adults aged 18 and over. One of the questions was, How manycups of coffee, if any, do you drink on an average day? The following table shows theresults obtained (Gallup website, August 6, 2012). Number of Cups per Day Number of Responses 0 365 1 264 2 193 3 91 4 or more 101 Define a random variable x = number of cups of coffee consumed on an average day. Let x = 4 represent four or more cups. a. Develop a probability distribution for x. b. Compute the expected value of x. c. Compute the variance of x. d. Suppose we are only interested in adults who drink at least one cup of coffee on an average day. For this group, let y = the number of cups of coffee consumed on anaverage day. Compute the expected value of y and compare it to the expected value of x.The J. R. Ryland Computer Company is considering a plant expansion to enable thecompany to begin production of a new computer product. The companys president must determine whether to make the expansion a medium- or large-scale project. Demand for the new product is uncertain, which for planning purposes may be low demand, mediumdemand, or high demand. The probability estimates for demand are .20, .50, and .30, respectively. Letting x and y indicate the annual profit in thousands of dollars, the firms plannersdeveloped the following profit forecasts for the medium- and large-scale expansion projects. Medium-Scale Expansion Profit Large-Scale Expansion Profit x f (x) y f (y) Low 50 .20 0 .20 Demand Medium 150 .50 100 .50 High 200 .30 300 .30 a. Compute the expected value for the profit associated with the two expansion alternatives. Which decision is preferred for the objective of maximizing the expectedprofit? b. Compute the variance for the profit associated with the two expansion alternatives.which decision is preferred for the objective of minimizing the risk or uncertainty?Given below is a bivariate distribution for the random variables x and y. f(x, y) x y .2 50 80 .5 30 50 .3 40 60 a. Compute the expected value and the variance for x and y. b. Develop a probability distribution for x + y. c. Using the result of part (b), compute E(x + y) and Var (x + y). d. Compute the covariance and correlation for x and y. Are x and y positively related,negatively related, or unrelated? e. Is the variance of the sum of x and y bigger, smaller, or the same as the sum of theindividual variances? Why?A person is interested in constructing a portfolio. Two stocks are being considered. Letx = percent return for an investment in stock 1, and y = percent return for an investment instock 2. The expected return and variance for stock 1 are E(x) = 8.45% and Var (x) = 25.The expected return and variance for stock 2 are E(y) = 3.20% and Var (y) = 1. The covariance between the returns is xy = 3. a. What is the standard deviation for an investment in stock 1 and for an investment instock 2? Using the standard deviation as a measure of risk, which of these stocks isthe riskier investment? b. What is the expected return and standard deviation, in dollars, for a person who invests500 in stock 1? c. What is the expected percent return and standard deviation for a person who constructsa portfolio by investing 50% in each stock? d. What is the expected percent return and standard deviation for a person who constructsa portfolio by investing 70% in stock 1 and 30% in stock 2? e. Compute the correlation coefficient for x and y and comment on the relationshipbetween the returns for the two stocks.The Chamber of Commerce in a Canadian city has conducted an evaluation of 300 restaurants in its metropolitan area. Each restaurant received a rating on a 3-point scale on typicalmeal price (1 least expensive to 3 most expensive) and quality (1 lowest quality to 3 greatestquality). A crosstabulation of the rating data is shown below. Forty-two of the restaurants received a rating of 1 on quality and 1 on meal price, 39 of the restaurants received a rating of 1 on quality and 2 on meal price, and so on. Forty-eight of the restaurants received thehighest rating of 3 on both quality and meal price. Quality (x) Meal Price (y) 1 2 3 Total 1 42 39 3 84 2 33 63 54 150 3 3 15 48 66 Total 78 117 105 300 a. Develop a bivariate probability distribution for quality and meal price of a randomly selected restaurant in this Canadian city. Let x = quality rating and y = mealprice. b. Compute the expected value and variance for quality rating, x. c. Compute the expected value and variance for meal price, y. d. The Var(x + y) = 1.6691. Compute the covariance of x and y. What can you say about the relationship between quality and meal price? Is this what you wouldexpect? e. Compute the correlation coefficient between quality and meal price. What is thestrength of the relationship? Do you suppose it is likely to find a low-cost restaurantin this city that is also high quality? Why or why not?PortaCom has developed a design for a high-quality portable printer. The two keycomponents of manufacturing cost are direct labor and parts. During a testing period,the company has developed prototypes and conducted extensive product tests with thenew printer. PortaComs engineers have developed the bivariate probability distribution shown below for the manufacturing costs. Parts cost (in dollars) per printer isrepresented by the random variable x and direct labor cost (in dollars) per printer isrepresented by the random variable y. Management would like to use this probabilitydistribution to estimate manufacturing costs. Parts (x) Direct Labor (y) 43 45 48 Total 85 0.05 0.2 0.2 0.45 95 0.25 0.2 0.1 0.55 Total 0.30 0.4 0.3 1.00 a. Show the marginal distribution of direct labor cost and compute its expected value,variance, and standard deviation. b. Show the marginal distribution of parts cost and compute its expected value, variance,and standard deviation. c. Total manufacturing cost per unit is the sum of direct labor cost and parts cost. Showthe probability distribution for total manufacturing cost per unit. d. Compute the expected value, variance, and standard deviation of total manufacturingcost per unit. e. Are direct labor and parts costs independent? Why or why not? If you conclude thatthey are not, what is the relationship between direct labor and parts cost? f. PortaCom produced 1500 printers for its product introduction. The total manufacturing cost was 198,350. Is that about what you would expect? If it is higher or lower,what do you think may have caused it?J.P. Morgan Asset Management publishes information about financial investments. Overthe past 10 years, the expected return for the SP 500 was 5.04% with a standard deviation of 19.45% and the expected return over that same period for a core bonds fund was5.78% with a standard deviation of 2.13% (J.P. Morgan Asset Management, Guide to theMarkets, 1st Quarter, 2012). The publication also reported that the correlation betweenthe SP 500 and core bonds is .32. You are considering portfolio investments that arecomposed of an SP 500 index fund and a core bonds fund. a. Using the information provided, determine the covariance between the SP 500 andcore bonds. b. Construct a portfolio that is 50% invested in an SP 500 index fund and 50% in a corebonds fund. In percentage terms, what are the expected return and standard deviationfor such a portfolio? c. Construct a portfolio that is 20% invested in an SP 500 index fund and 80% investedin a core bonds fund. In percentage terms, what are the expected return and standarddeviation for such a portfolio? d. Construct a portfolio that is 80% invested in an SP 500 index fund and 20% investedin a core bonds fund. In percentage terms, what are the expected return and standarddeviation for such a portfolio? e. which of the portfolios in parts (b), (c), and (d) has the largest expected return? whichhas the smallest standard deviation? which of these portfolios is the best investmentalternative? f. Discuss the advantages and disadvantages of investing in the three portfolios in parts(b), (c), and (d). would you prefer investing all your money in the SP 500 index, thecore bonds fund, or one of the three portfolios? why?In addition to the information in exercise 29 on the SP 500 and core bonds, J.P. Morgan Asset Management reported that the expected return for real estate investment trusts(REITs) was 13.07% with a standard deviation of 23.17% (J.P. Morgan Asset Management, Guide to the Markets, 1st quarter, 2012). The correlation between the SP 500 andREITs is .74 and the correlation between core bonds and REITs is .04. You are considering portfolio investments that are composed of an SP 500 index fund and REITs as wellas portfolio investments composed of a core bonds fund and REITs. a. Using the information provided here and in exercise 29, determine the covariancebetween the SP 500 and REITs and between core bonds and REITs. b. Construct a portfolio that is 50% invested in an SP 500 fund and 50% invested inREITs. In percentage terms, what are the expected return and standard deviation forsuch a portfolio? c. Construct a portfolio that is 50% invested in a core bonds fund and 50% invested inREITs. In percentage terms, what are the expected return and standard deviation forsuch a portfolio? d. Construct a portfolio that is 80% invested in a core bonds fund and 20% invested inREITs. In percentage terms, what are the expected return and standard deviation forsuch a portfolio? e. which of the portfolios in parts (b), (c), and (d) would you recommend to anaggressive investor? which would you recommend to a conservative investor? why?Consider a binomial experiment with two trials and p = .4. a. Draw a tree diagram for this experiment (see Figure 5.3). b. Compute the probability of one success, f(1). c. Compute f(0). d. Compute f (2). e. Compute the probability of at least one success. f. Compute the expected value, variance, and standard deviation.Consider a binomial experiment with n = 10 and p = .10. a. Compute f(0). b. Compute f(2). c. Compute P(x 2). d. Compute P(x 1). e. Compute E(x). f. Compute Var(x) and .Consider a binomial experiment with n = 20 and p = .70. a. Compute f(12). b. Compute f(16). c. Compute P(x 16). d. Compute P(x 15). e. Compute E(x). f. Compute Var (x) and .For its Music 360 survey, Nielsen Co. asked teenagers and adults how each group has listenedto music in the past 12 months. Nearly two-thirds of U.S. teenagers under the age of 18 say theyuse Google Inc.s video-sharing site to listen to music and 35% of the teenagers said they usePandora Media Inc.s custom online radio service (The Wall Street Journal, August 14, 2012).Suppose 10 teenagers are selected randomly to be interviewed about how they listen to music. a. Is randomly selecting 10 teenagers and asking whether or not they use Pandora MediaInc.s online service a binomial experiment? b. What is the probability that none of the 10 teenagers use Pandora Media Inc.s onlineradio service? c. What is the probability that 4 of the 10 teenagers use Pandora Media Inc.s online radioservice? d. What is the probability that at least 2 of the 10 teenagers use Pandora Media Inc.sonline radio service?The Center for Medicare and Medical Services reported that there were 295,000 appealsfor hospitalization and other Part A Medicare service. For this group, 40% of first-roundappeals were successful (The Wall Street Journal, October 22, 2012). Suppose 10 first-round appeals have just been received by a Medicare appeals office. a. Compute the probability that none of the appeals will be successful. b. Compute the probability that exactly one of the appeals will be successful. c. What is the probability that at least two of the appeals will be successful? d. What is the probability that more than half of the appeals will be successful?When a new machine is functioning properly, only 3% of the items produced are defective.Assume that we will randomly select two parts produced on the machine and that we areinterested in the number of defective parts found. a. Describe the conditions under which this situation would be a binomial experiment. b. Draw a tree diagram similar to Figure 5.4 showing this problem as a two-trial experiment. c. How many experimental outcomes result in exactly one defect being found? d. Compute the probabilities associated with finding no defects, exactly one defect, andtwo defects.According to a 2013 study by the Pew Research Center, 15% of adults in the United Statesdo not use the Internet (Pew Research Center website, December, 15, 2014). Suppose that10 adults in the United States are selected randomly. a. Is the selection of the 10 adults a binomial experiment? Explain. b. What is the probability that none of the adults use the Internet? c. What is the probability that 3 of the adults use the Internet? d. What is the probability that at least 1 of the adults uses the Internet?Military radar and missile detection systems are designed to warn a country of an enemy attack. A reliability question is whether a detection system will be able to identify an attack andissue a warning. Assume that a particular detection system has a .90 probability of detectinga missile attack. Use the binomial probability distribution to answer the following questions. a. What is the probability that a single detection system will detect an attack? b. If two detection systems are installed in the same area and operate independently, whatis the probability that at least one of the systems will detect the attack? c. If three systems are installed, what is the probability that at least one of the systemswill detect the attack? d. Would you recommend that multiple detection systems be used? Explain.Market-share-analysis company Net Applications monitors and reports on Internetbrowser usage. According to Net Applications, in the summer of 2014, Googles Chromebrowser exceeded a 20% market share for the first time, with a 20.37% share of thebrowser market (Forbes website, December 15, 2014). For a randomly selected group of20 Internet browser users, answer the following questions. a. Compute the probability that exactly 8 of the 20 Internet browser users use Chromeas their Internet browser. b. Compute the probability that at least 3 of the 20 Internet browser users use Chrome astheir Internet browser. c. For the sample of 20 Internet browser users, compute the expected number of Chromeusers. d. For the sample of 20 Internet browser users, compute the variance and standard deviation for the number of Chrome users.A study conducted by the Pew Research Center showed that 75% of 18- to 34-year-olds living with their parents say they contribute to household expenses (The Wall Street Journal,October 22, 2012). Suppose that a random sample of fifteen 18- to 34-year-olds living withtheir parents is selected and asked if they contribute to household expenses. a. Is the selection of the fifteen 18- to 34-year-olds living with their parents a binomialexperiment? Explain. b. If the sample shows that none of the fifteen 18- to 34-year-olds living with their parentscontribute to household expenses, would you question the results of the Pew ResearchStudy? Explain. c. What is the probability that at least 10 of the fifteen 18- to 34-year-olds living with theirparents contribute to household expenses?A university found that 20% of its students withdraw without completing the introductorystatistics course. Assume that 20 students registered for the course. a. Compute the probability that 2 or fewer will withdraw. b. Compute the probability that exactly 4 will withdraw. c. Compute the probability that more than 3 will withdraw. d. Compute the expected number of withdrawals.A Gallup Poll showed that 30% of Americans are satisfied with the way things are going inthe United States (Gallup website, September 12, 2012). Suppose a sample of 20 Americansis selected as part of a study of the state of the nation. a. Compute the probability that exactly 4 of the 20 Americans surveyed are satisfied withthe way things are going in the United States. b. Compute the probability that at least 2 of the Americans surveyed are satisfied withthe way things are going in the United States. c. For the sample of 20 Americans, compute the expected number of Americans who aresatisfied with the way things are going in the United States. d. For the sample of 20 Americans, compute the variance and standard deviation of thenumber of Americans who are satisfied with the way things are going in the United States.According to a 2010 study conducted by the Toronto-based social media analytics firm Sysomos, 71% of all tweets get no reaction. That is, these are tweets that are not replied to or retweeted (Sysomos website, January 5, 2015). Suppose we randomly select 100 tweets. a. What is the expected number of these tweets with no reaction? b. what are the variance and standard deviation for the number of these tweets with noreaction?Consider a Poisson distribution with = 3. a. write the appropriate Poisson probability function. b. Compute f(2). c. Compute f(1). d. Compute P(x 2).Consider a Poisson distribution with a mean of two occurrences per time period. a. Write the appropriate Poisson probability function. b. What is the expected number of occurrences in three time periods? c. Write the appropriate Poisson probability function to determine the probability of xoccurrences in three time periods. d. Compute the probability of two occurrences in one time period. e. Compute the probability of six occurrences in three time periods. f. Compute the probability of five occurrences in two time periods.Phone calls arrive at the rate of 48 per hour at the reservation desk for Regional Airways. a. Compute the probability of receiving three calls in a 5-minute interval of time. b. Compute the probability of receiving exactly 10 calls in 15 minutes. c. Suppose no calls are currently on hold. If the agent takes 5 minutes to complete thecurrent call, how many callers do you expect to be waiting by that time? What is theprobability that none will be waiting? d. If no calls are currently being processed, what is the probability that the agent can take3 minutes for personal time without being interrupted by a call?During the period of time that a local university takes phone-in registrations, calls come inat the rate of one every two minutes. a. What is the expected number of calls in one hour? b. What is the probability of three calls in five minutes? c. What is the probability of no calls in a five-minute period?In 2011, New York City had a total of 11,232 motor vehicle accidents that occurred onMonday through Friday between the hours of 3 p.m. and 6 p.m. (New York State Department of Motor Vehicles website, October 24, 2012). This corresponds to mean of 14.4accidents per hour. a. Compute the probability of no accidents in a 15-minute period. b. Compute the probability of at least one accident in a 15-minute period. c. Compute the probability of four or more accidents in a 15-minute period.Airline passengers arrive randomly and independently at the passenger-screening facilityat a major international airport. The mean arrival rate is 10 passengers per minute. a. Compute the probability of no arrivals in a one-minute period. b. Compute the probability that three or fewer passengers arrive in a one-minute period. c. Compute the probability of no arrivals in a 15-second period. d. Compute the probability of at least one arrival in a 15-second period.According to the National Oceanic and Atmospheric Administration (NOAA), the state ofColorado averages 18 tornadoes every June (NOAA website, November 8, 2012). (Note:There are 30 days in June.) a. Compute the mean number of tornadoes per day. b. Compute the probability of no tornadoes during a day. c. Compute the probability of exactly one tornado during a day. d. Compute the probability of more than one tornado during a day.Over 500 million tweets are sent per day (Digital Marketing Ramblings website,December 15, 2014). Assume that the number of tweets per hour follows a Poisson distribution and that Bob receives on average 7 tweets during his lunch hour. a. What is the probability that Bob receives no tweets during his lunch hour? b. What is the probability that Bob receives at least 4 tweets during his lunch hour? c. What is the expected number of tweets Bob receives during the first 30 minutes of hislunch hour? d. What is the probability that Bob receives no tweets during the first 30 minutes of hislunch hour?Suppose N = 10 and r = 3. Compute the hypergeometric probabilities for the followingvalues of n and x. a. n = 4, x = 1. b. n = 2, x = 2. c. n = 2, x = 0. d. n = 4, x = 2. e. n = 4, x = 4.Suppose N = 15 and r = 4. What is the probability of x = 3 for n = 10?A recent survey showed that a majority of Americans plan on doing their holiday shoppingonline because they dont want to spend money on gas driving from store to store (SOASTAwebsite, October 24, 2012). Suppose we have a group of 10 shoppers; 7 prefer to do theirholiday shopping online and 3 prefer to do their holiday shopping in stores. A randomsample of 3 of these 10 shoppers is selected for a more in-depth study of how the economyhas impacted their shopping behavior. a. What is the probability that exactly 2 prefer shopping online? b. What is the probability that the majority (either 2 or 3) prefer shopping online?Blackjack, or twenty-one as it is frequently called, is a popular gambling game played inLas Vegas casinos. A player is dealt two cards. Face cards (jacks, queens, and kings) andtens have a point value of 10. Aces have a point value of 1 or 11. A 52-card deck contains16 cards with a point value of 10 (jacks, queens, kings, and tens) and four aces. a. What is the probability that both cards dealt are aces or 10-point cards? b. What is the probability that both of the cards are aces? c. What is the probability that both of the cards have a point value of 10? d. A blackjack is a 10-point card and an ace for a value of 21. Use your answers to parts(a), (b), and (c) to determine the probability that a player is dealt blackjack. (Hint:Part (d) is not a hypergeometric problem. Develop your own logical relationship asto how the hypergeometric probabilities from parts (a), (b), and (c) can be combinedto answer this question.)Axline Computers manufactures personal computers at two plants, one in Texas and theother in Hawaii. The Texas plant has 40 employees; the Hawaii plant has 20. A randomsample of 10 employees is to be asked to fill out a benefits questionnaire. a. What is the probability that none of the employees in the sample work at the plant inHawaii? b. What is the probability that 1 of the employees in the sample works at the plant inHawaii? c. What is the probability that 2 or more of the employees in the sample work at the plantin Hawaii? d. What is the probability that 9 of the employees in the sample work at the plant in Texas?The Zagat Restaurant Survey provides food, decor, and service ratings for some of thetop restaurants across the United States. For 15 restaurants located in Boston, the averageprice of a dinner, including one drink and tip, was 48.60. You are leaving on a business trip to Boston and will eat dinner at three of these restaurants. Your company willreimburse you for a maximum of 50 per dinner. Business associates familiar with theserestaurants have told you that the meal cost at one-third of these restaurants will exceed50. Suppose that you randomly select three of these restaurants for dinner. a. What is the probability that none of the meals will exceed the cost covered by yourcompany? b. What is the probability that one of the meals will exceed the cost covered by yourcompany? c. What is the probability that two of the meals will exceed the cost covered by yourcompany? d. What is the probability that all three of the meals will exceed the cost covered by yourcompany?The Troubled Asset Relief Program (TARP), passed by the U.S. Congress in October 2008,provided 700 billion in assistance for the struggling U.S. economy. Over 200 billion wasgiven to troubled financial institutions with the hope that there would be an increase inlending to help jump-start the economy. But three months later, a Federal Reserve surveyfound that two-thirds of the banks that had received TARP funds had tightened terms forbusiness loans (The Wall Street Journal, February 3, 2009). Of the 10 banks that were thebiggest recipients of TARP funds, only 3 had actually increased lending during this period. Increased Lending Decreased Lending BBT Bank of America Sun Trust Banks Capital One U.S. Bancorp Citigroup Fifth Third Bancorp J.P. Morgan Chase Regions FinancialWells Fargo For the purposes of this exercise, assume that you will randomly select 3 of these 10 banks for a study that will continue to monitor bank lending practices. Let x be a random variableindicating the number of banks in the study that had increased lending. a. What is f(0)? What is your interpretation of this value? b. What is f(3)? What is your interpretation of this value? c. Compute f(1) and f(2). Show the probability distribution for the number of banks inthe study that had increased lending. What value of x has the highest probability? d. What is the probability that the study will have at least one bank that had increasedlending? e. Compute the expected value, variance, and standard deviation for the random variable.The U.S. Coast Guard (USCG) provides a wide variety of information on boating accidentsincluding the wind condition at the time of the accident. The following table shows theresults obtained for 4401 accidents (USCG website, November 8, 2012). Wind Condition Percentage of Accidents None 9.6 Light 57.0 Moderate 23.8 Strong 7.7 Storm 1.9 Let x be a random variable reflecting the known wind condition at the time of each accident. Set x = 0 for none, x = 1 for light, x = 2 for moderate, x = 3 for strong, andx = 4 for storm. a. Develop a probability distribution for x. b. Compute the expected value of x. c. Compute the variance and standard deviation for x. Comment on what your results imply about the wind conditions during boating accidents.The Car Repair Ratings website provides consumer reviews and ratings for garages inthe United States and Canada. The time customers wait for service to be completed is oneof the categories rated. The following table provides a summary of the wait-time ratings (1 = Slow/Delays; 10 = Quick/On Time) for 40 randomly selected garages located in the province of Ontario, Canada (Car Repair Ratings website, November 14, 2012). Wait-Time Rating Number of Garages 1 6 2 2 3 3 4 2 5 5 6 2 7 4 8 5 9 5 10 6 a. Develop a probability distribution for x = wait-time rating. b. Any garage that receives a wait-time rating of at least 9 is considered to provide outstanding service. If a consumer randomly selects one of the 40 garages for their next car service,what is the probability the garage selected will provide outstanding wait-time service? c. What is the expected value and variance for x? Suppose that 7 of the 40 garages reviewed were new car dealerships. Of the 7 new cardealerships, two were rated as providing outstanding wait-time service. Compare thelikelihood of a new car dealership achieving an outstanding wait-time service ratingas compared to other types of service providers.The budgeting process for a midwestern college resulted in expense forecasts for the coming year (in millions) of 9, 10, 11, 12, and 13. Because the actual expenses areunknown, the following respective probabilities are assigned: .3, .2, .25, .05, and .2. a. Show the probability distribution for the expense forecast. b. what is the expected value of the expense forecast for the coming year? c. what is the variance of the expense forecast for the coming year? If income projections for the year are estimated at 12 million, comment on thefinancial position of the college.A bookstore at the Hartsfield-Jackson Airport in Atlanta sells reading materials (paperback books, newspapers, magazines) as well as snacks (peanuts, pretzels, candy, etc.). Apoint-of-sale terminal collects a variety of information about customer purchases. Shownbelow is a table showing the number of snack items and the number of items of readingmaterial purchased by the most recent 600 customers. 0 Reading Material 1 2 0 0 60 18 Snacks 1 240 90 30 2 120 30 12 a. Using the data in the table construct an empirical discrete bivariate probability distribution for x = number of snack items and y = number of reading materials in arandomly selected customer purchase. what is the probability of a customer purchase consisting of one item of reading materials and two snack items? what is theprobability of a customer purchasing one snack item only? why is the probabilityf(x = 0, y = 0) = 0? b. Show the marginal probability distribution for the number of snack items purchased.Compute the expected value and variance. c. What is the expected value and variance for the number of reading materials purchasedby a customer? d. Show the probability distribution for t = total number of items in a customer purchase.Compute its expected value and variance. Compute the covariance and correlation coefficient between x and y. What is therelationship, if any, between the number of reading materials and number of snackspurchased on a customer visit?The Knowles/Armitage (KA) group at Merrill Lynch advises clients on how to create adiversified investment portfolio. One of the investment alternatives they make available toclients is the All World Fund composed of global stocks with good dividend yields. One oftheir clients is interested in a portfolio consisting of investment in the All World Fund and atreasury bond fund. The expected percent return of an investment in the All World Fund is7.80% with a standard deviation of 18.90%. The expected percent return of an investmentin a treasury bond fund is 5.50% and the standard deviation is 4.60%. The covariance of aninvestment in the All World Fund with an investment in a treasury bond fund is 12.4. a. Which of the funds would be considered the more risky? Why? b. If KA recommends that the client invest 75% in the All World Fund and 25% in thetreasury bond fund, what is the expected percent return and standard deviation for sucha portfolio? What would be the expected return and standard deviation, in dollars, fora client investing 10,000 in such a portfolio? c. If KA recommends that the client invest 25% in the All World Fund and 75% inthe treasury bond fund, what is the expected return and standard deviation for such aportfolio? What would be the expected return and standard deviation, in dollars, for aclient investing 10,000 in such a portfolio? Which of the portfolios in parts (b) and (c) would you recommend for an aggressive investor? Which would you recommend for a conservative investor? Why?The Pew Research Center surveyed adults who own/use the following technologies:Internet, smartphone, email, and land-line phone (USA Today, March 26, 2014) andasked which of these technologies would be very hard to give up. The followingresponses were obtained: Internet 53%, smartphone 49%, email 36%, and land-linephone 28%. a. If 20 adult Internet users are surveyed, what is the probability that 3 users will reportthat it would be very hard to give it up? b. If 20 adults who own a land-line phone are surveyed, what is the probability that 5 orfewer will report that it would be very hard to give it up? c. If 2000 owners of smartphones were surveyed, what is the expected number that willreport that it would be very hard to give it up? If 2000 users of email were surveyed, what is expected number that will report thatit would be very hard to give it up? What is the variance and standard deviation?The following table shows the percentage of individuals in each age group who use anonline tax program to prepare their federal income tax return (CompleteTax website,November 9, 2012). Age Online Tax Program (%) 1834 16 3544 12 4554 10 5564 8 65 + 2 Suppose a follow-up study consisting of personal interviews is to be conducted to determine the most important factors in selecting a method for filing taxes. a. How many 1834-year-olds must be sampled to find an expected number of at least25 who use an online tax program to prepare their federal income tax return? b. How many 3544-year-olds must be sampled to find an expected number of at least25 who use an online tax program to prepare their federal income tax return? c. How many 65+-year-olds must be sampled to find an expected number of at least 25who use an online tax program to prepare their federal income tax return? d. If the number of 1834-year-olds sampled is equal to the value identified in part (a),what is the standard deviation of the percentage who use an online tax program? e. If the number of 3544-year-olds sampled is equal to the value identified in part (b),what is the standard deviation of the percentage who use an online tax program?Many companies use a quality control technique called acceptance sampling to monitor incoming shipments of parts, raw materials, and so on. In the electronics industry, componentparts are commonly shipped from suppliers in large lots. Inspection of a sample of n components can be viewed as the n trials of a binomial experiment. The outcome for each component tested (trial) will be that the component is classified as good or defective. ReynoldsElectronics accepts a lot from a particular supplier if the defective components in the lot donot exceed 1%. Suppose a random sample of five items from a recent shipment is tested. a. Assume that 1% of the shipment is defective. Compute the probability that no itemsin the sample are defective. b. Assume that 1% of the shipment is defective. Compute the probability that exactly oneitem in the sample is defective. c. What is the probability of observing one or more defective items in the sample if 1%of the shipment is defective? would you feel comfortable accepting the shipment if one item was found to bedefective? Why or why not?PBS News Hour reported that 39.4% of Americans between the ages of 25 and 64 haveat least a two-year college degree (PBS website, December 15, 2014). Assume that 50Americans between the ages of 25 and 64 are selected randomly. a. What is the expected number of people with at least a two-year college-degree? b. What are the variance and standard deviation for the number of people with at least atwo-year college degree?Mahoney Custom Home Builders, Inc. of Canyon Lake, Texas, asked visitors to theirwebsite what is most important when choosing a home builder. Possible responses werequality, price, customer referral, years in business, and special features. Results showedthat 23.5% of the respondents chose price as the most important factor (Mahoney CustomHomes website, November 13, 2012). Suppose a sample of 200 potential home buyers inthe Canyon Lake area was selected. a. How many people would you expect to choose price as the most important factor when choosing a home builder? b. What is the standard deviation of the number of respondents who would choose priceas the most important factor in selecting a home builder? What is the standard deviation of the number of respondents who do not list price asthe most important factor in selecting a home builder?Cars arrive at a car wash randomly and independently; the probability of an arrival is thesame for any two time intervals of equal length. The mean arrival rate is 15 cars per hour.What is the probability that 20 or more cars will arrive during any given hour of operation?A new automated production process averages 1.5 breakdowns per day. Because of thecost associated with a breakdown, management is concerned about the possibility of having three or more breakdowns during a day. Assume that breakdowns occur randomly,that the probability of a breakdown is the same for any two time intervals of equal length,and that breakdowns in one period are independent of breakdowns in other periods. Whatis the probability of having three or more breakdowns during a day?A regional director responsible for business development in the state of Pennsylvania isconcerned about the number of small business failures. If the mean number of small business failures per month is 10, what is the probability that exactly 4 small businesses willfail during a given month? Assume that the probability of a failure is the same for any twomonths and that the occurrence or nonoccurrence of a failure in any month is independentof failures in any other month.Customer arrivals at a bank are random and independent; the probability of an arrival in anyone-minute period is the same as the probability of an arrival in any other one-minute period.Answer the following questions, assuming a mean arrival rate of three customers per minute. a. What is the probability of exactly three arrivals in a one-minute period? b. What is the probability of at least three arrivals in a one-minute period?A deck of playing cards contains 52 cards, four of which are aces. What is the probabilitythat the deal of a five-card hand provides a. A pair of aces? b. Exactly one ace? c. No aces? d. At least one ace?U.S. News World Reports ranking of Americas best graduate schools of businessshowed Harvard University and Stanford University in a tie for first place. In addition,7 of the top 10 graduate schools of business showed students with an average undergraduate grade point average (GPA) of 3.50 or higher (Americas Best Graduate Schools, 2009edition, U.S. News World Report). Suppose that we randomly select 2 of the top 10graduate schools of business. a. What is the probability that exactly one school has students with an average undergraduate GPA of 3.50 or higher? b. What is the probability that both schools have students with an average undergraduateGPA of 3.50 or higher? c. What is the probability that neither school has students with an average undergraduateGPA of 3.50 or higher?1CP The random variable x is known to be uniformly distributed between 1.0 and 1.5. a. Show the graph of the probability density function. b. Compute P(x = 1.25). c. Compute P(1.0 x 1.25). d. Compute P(1.20 x 1.5).The random variable x is known to be uniformly distributed between 10 and 20. a. Show the graph of the probability density function. b. Compute P(x 15). c. Compute P(12 x 18). d. Compute E(x). e. Compute Var(x).

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