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All Textbook Solutions for Essentials Of Statistics For Business & Economics

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 company’s 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). How many elements are in this data set? How many variables are in this data set? Which variables are categorical and which variables are quantitative? What type of measurement scale is used for each of the variables? Refer to Table 1.6. What is the average cost for the tablets? Compare the average cost of tablets with a Windows operating system to the average cost of tablets with an Android operating system. What percentage of tablets use a CPU manufactured by TI OMAP? What percentage of tablets use an Android operating system? 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 Talk Time, which variables are categorical and which variables are quantitative? c. What scale of measurement is used for each variable?Summarizing Phone Data. Refer to the data set in Table 1.7. a. What is the average price for the phones? b. What is the average talk time for the phones? c. What percentage of the phones have a voice quality of excellent? TABLE 1.7 Data for Eight Phones 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.Airline Customer Satisfaction. Many service companies collect data via a follow-up survey of their customers. For example, to ascertain customer sentiment, Delta Air Lines sends an email to customers immediately following a flight. Among other questions, Delta asks: How likely are you to recommend Delta Air Lines to others? The possible responses are: a. Are the data collected by Delta in this example quantitative or categorical? 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 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?College-Educated Workers. Based on data from the U.S. Census Bureau, a Pew Research study showed that the percentage of employed individuals ages 2529 who are college educated is at an all-time high. The study showed that the percentage of employed individuals aged 2529 with at least a bachelors degree in 2016 was 40%. In the year 2000, this percentage was 32%, in 1985 it was 25%, and in 1964 it was only 16% (Pew Research website). a. What is the population being studied in each of the four years in which Pew has data? b. What question was posed to each respondent? c. Do responses to the question provide categorical or quantitative data?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). Do the responses for this statement provide categorical or quantitative data? Would it make more sense to use averages or percentages as a summary of the responses for this statement? What percentage of respondents strongly agree with allowing drivers of motor vehicles to talk on a hand-held cell phone while driving? Do the results indicate general support for or against allowing drivers of motor vehicles to talk on a hand-held cell phone while driving? Driverless Cars Expected Soon. A Gallup Poll utilizing a random sample of 1,503 adults ages 18 or older was conducted in April 2018. The survey indicated a majority of Americans (53%) say driverless cars will be common in the next 10 years (Gallup, FIGURE 1.7 Histogram of Survey Results on Driverless Cars https://news.gallup.com/poll/234152/americans-expect-driverless-cars-common-next-decade.aspx). The question asked was: Thinking about fully automated, driverless cars, cars that use technology to drive and do not need a human driver, based on what you have heard or read, how soon do you think driverless cars will be commonly used in the [United States]? Figure 1.7 shows a summary of results of the survey in a histogram indicating the percentage of the total responses in different time intervals. a. Are the responses to the survey question quantitative or categorical? b. How many of the respondents said that they expect driverless cars to be common in the next 10 years? c. How many respondents answered in the range 1620 years?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 What is the population being studied? Is the use of a questionnaire a good way to reach the population of passengers on incoming airline flights? Comment on each of the four questions in terms of whether it will provide categorical or quantitative data. Facebook Advertising Revenue. Figure 1.8 provides a bar chart showing the annual advertising revenue for Facebook from 2010 to 2017 (Facebook Annual Reports). a. What is the variable of interest? b. Are the data categorical or quantitative? c. Are the data time series or cross-sectional? d. Comment on the trend in Facebooks annual advertising revenue over time. FIGURE 1.8 Facebook Worldwide Advertising Revenue Rental Car Fleet Size. The following data show the number of rental cars in service (in thousands) for three rental car companies: Hertz, Avis, and Dollar over a three-year period (Auto Rental News website). 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. Comment on who appears to be the market share leader and how the market shares are changing over time. Construct a bar chart showing rental cars in service for 2010. Is this chart based on cross-sectional or time series data? Jewelry Sales. The U.S. Census Bureau tracks sales per month for various products and services through its Monthly Retail Trade Survey. Figure 1.9 shows monthly jewelry sales in millions of dollars for 2016. a. Are the data quantitative or categorical? b. Are the data cross-sectional or time series? c. Which four months have the highest sales? d. Why do you think the answers to part c might be the highest four months?Athletic Shoe Sales. Skechers U.S.A., Inc., is a performance footwear company headquartered in Manhattan Beach, California. The sales revenue for Skechers over a four-year period are as follows: Are these cross-sectional or time-series data? FIGURE 1.9 Estimated Monthly Jewelry Sales in the United States for 2016 Source: The U.S. Census Bureau tracks sales per month for various products and services through its Monthly Retail Trade Survey (https://www.census.gov/retail/mrts/historic_releases.html) Construct a bar graph similar to Figure 1.2 B. What can you say about how Skecher’s sales are changing over these four years? 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. What is the population of interest in this study? Is annual income a categorical or quantitative variable? Is ownership of an American Express card a categorical or quantitative variable? Does this study involve cross-sectional or time series data? Describe any statistical inferences Bloomberg Businessweek might make on the basis of the survey. A survey of 131 investment managers in Barron’s 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. Cite two descriptive statistics. Make an inference about the population of all investment managers concerning the average return expected on equities over the next 12 months. 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. This study compared two populations. What were the populations? Do you suppose the data were obtained in a survey or an experiment? 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. 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? 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 (Belter 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?Teenage Cell Phone Use. 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 73% of teens aged 1317 have a smartphone, 15% have a basic phone and 12% have no phone. The study also asked the respondents how they communicated with their closest friend. Of those with a smartphone, 58% responded texting, 17% social media and 10% phone calls. Of those with no smartphone, 25% responded texting, 29% social media and 21% phone calls (Pew Research Center website, October 2015). a. One statistic (58%) concerned the use of texting to contact his/her closest friend, if the teen owns a smartphone. To what population is that applicable? b. Another statistic (25%) concerned the use of texting by those who do not own a smartphone. To what population is that applicable? c. Do you think the Pew researchers conducted a census or a sample survey to obtain their results? Why?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? The average midterm grade for the sample of five students is 77. The average midterm grade for all students who took the exam is 77. An estimate of the average midterm grade for all students who took the exam is 77. More than half of the students who lake this exam will score between 70 and 85. If five other students are included in the sample, their grades will be between 65 and 90. Comparing Compact SUVs. Consumer Reports evaluates products for consumers. The file CompactSUV contains the data shown in Table 1.8 for 15 compact sports utility vehicles (SUVs) from the 2018 model line (Consumer Reports website): Makemanufacturer Modelname of the model Overall scoreawarded based on a variety of measures, including those in this data set RecommendedConsumer Reports recommends the vehicle or not Owner satisfactionsatisfaction on a five-point scale based on the percentage of owners who would purchase the vehicle again ( , , 0, +, + +). Overall miles per gallonmiles per gallon achieved in a 150-mile test trip Acceleration (060 sec)time in seconds it takes vehicle to reach 60 miles per hour from a standstill with the engine idling a. How many variables are in the data set? b. Which of the variables are categorical, and which are quantitative? c. What percentage of these 15 vehicles are recommended? d. What is the average of the overall miles per gallon across all 15 vehicles? e. For owner satisfaction, construct a bar chart similar to Figure 1.4. f. Show the frequency distribution for acceleration using the following intervals: 7.07.9, 8.08.9, 9.09.9, and 10.010.9. Construct a histogram similar to Figure 1.5.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. 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.Most Visited Websites. In a recent report, the top five most-visited English-language websites were google.com (GOOG), facebook.com (FB), youtube.com (YT), yahoo.com (YAH), and wikipedia.com (WIKI). The most-visited websites for a sample of 50 Internet users are shown in the following table: a. Are these data categorical or quantitative? b. Provide frequency and percent frequency distributions. c. On the basis of the sample, which website is most frequently visited website for Internet users? Which is second?Most Popular Last Names. In alphabetical order, the six most common last names in the United States in 2018 are Brown, Garcia, Johnson, Jones, Smith, and Williams (United States Census Bureau website). 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 sorted bar chart d. A pie chart e. Based on these data, what are the three most common last names? Which type of chart makes this most apparent?Top Rated Television Show Networks. Nielsen Media Research tracks the top-rated television shows. The following data show the television network that produced each of the 25 top-rated shows in the history of television. a. Construct a frequency distribution, percent frequency distribution, and bar chart for the data. b. Which networks have done the best in terms of presenting top-rated television shows? Compare the performance of ABC, CBS, and NBC.Airline Customer Satisfaction Survey. Many airlines use surveys to collect data on customer satisfaction related to flight experiences. Completing a flight, customers receive an email asking them to 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. Suppose that 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 Farmers: 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). Construct frequency and relative frequency distributions to summarize the data. What position provides the most Hall of Farmers? What position provides the fewest Hall of Farmers? What outfield position (L, C, or R) provides the most Hall of Farmers? Compare infielders (1, 2, 3, and S) to outfielders (L, C, and R). Degrees Awarded Annually. Nearly 1.9 million bachelors degrees and over 758,000 masters degrees are awarded annually by U.S. postsecondary institutions as of 2018 (National Center for Education Statistics website). 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?Online Hotel Ratings. TripAdvisor is one of many online websites that provides ratings for hotels throughout the world. Ratings provided by 649 guests at the Lakeview Hotel can be found in the file HotelRatings. 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. Suppose that results for 1679 guests who stayed at the Timber Hotel provided the following frequency distribution. Compare the ratings for the Timber Hotel with the results obtained for the Lakeview Lodge.Consider the following data. a. Develop a frequency distribution using classes of 1214, l517, l820, 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. Construct a cumulative frequency distribution and a cumulative relative frequency distribution.Construct a histogram for the data in exercise 12. 12. Consider the following frequency distribution. Construct a cumulative frequency distribution and a cumulative relative frequency distribution.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. Construct a stem-and-leaf display for the following data. Use a leaf unit of 10. A doctor’s 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. Use classes of 0–4, 5–9, and so on in the following: Show the frequency distribution. Show the relative frequency distribution. Show the cumulative frequency distribution. Show the cumulative relative frequency distribution. What proportion of patients needing emergency service wait 9 minutes or less? NBA Total Player Ratings. 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 an NBA season (CBSSports.com website). Use classes starting at 10 and ending at 30 in increments of 2 for PPG in the following. Show the frequency distribution. Show the relative frequency distribution. Show the cumulative percent frequency distribution. Develop a histogram for the average number of points scored per game. Do the data appear to be skewed? Explain. What percentage of the players averaged at least 20 points per game? Busiest North American Airports. Based on the total passenger traffic, the airports in the following list are the 20 busiest airports in North America in 2018 (The World Almanac). a. Which is busiest airport in terms of total passenger traffic? Which is the least busy airport in terms of total passenger traffic? b. Using a class width of 10, develop a frequency distribution of the data starting with 3039.9, 4049.9, 5059.9, and so on. c. Prepare a histogram. Interpret the histogram.CEO Time in Meetings. The London School of Economics and the Harvard Business School have conducted studies of how chief executive officers (CEOs) spend their time. These studies have found that CEOs spend many hours per week in meetings that include conference calls, business meals, and public events. Suppose that the data below show 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.Largest University Endowments. University endowments are financial assets that are donated by supporters to be used to provide income to universities. There is a large discrepancy in the size of university endowments. The following table provides a listing of many of the universities that have the largest endowments as reported by the National Association of College and University Business Officers in 2017. Summarize the data by constructing the following: A frequency distribution (classes 0–1.9, 2.0–3.9, 4.0–5.9, 6.0–7.9, and so on). A relative frequency distribution. A cumulative frequency distribution. A cumulative relative frequency distribution. What do these distributions tell you about the endowments of universities? Show a histogram. Comment on the shape of the distribution. What is the largest university endowment and which university holds it? Top U.S. Franchises. Entrepreneur magazine ranks franchises using performance measures such as growth rate, number of locations, startup costs, and financial stability. The number of locations for 20 U.S. franchises follows (The World Almanac). 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.Engineering School Graduate Salaries. The file EngineeringSalary contains the median starting salary and median mid-career salary (measured 10 years after graduation) for graduates from 19 engineering schools (The Wall Street Journal). Develop a stem-and-leaf display for both the median starting salary and the median mid-career salary. Comment on any differences you observe.Best Paying College Degrees. 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 hi ghest mid-career salary (America.EDU website). 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?Marathon Runner Ages. The Flying Pig is a marathon (26.2 mile long) running race held every year in Cincinnati, Ohio. Suppose that the following data show the ages for a sample of 40 marathon runners. 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. Develop a crosstabulation for the data, with x as the row variable and y as the column variable. Compute the row percentages. Compute the column percentages. 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?Daytona 500 Automobile Makes Average Speeds. 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 over a 25 year period (The 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?Daytona 500 Average Speeds of Winners. The following crosstabulation shows the average speed of the 25 winners by year of the Daytona 500 automobile race (The 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. Combine these two crosstabulations into one with Male and Female as the tow labels and Too Fast and Fine as the column labels. Which group shows the highest percentage saying that the greens are too fast? 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? 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? 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. Household Income Levels. 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, https://www.census.gov/data/tables/time-series/demo/income-poverty/cps-hinc.html). 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?Values of World’s Most Valuable Brands. Each year Forbes ranks the world’s 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). 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 brand’s 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. Prepare a crosstabulation of the data on Industry (rows) and Brand Value ($ billions). Use classes of 0–10, 10–20, 20–30, 30–40, 40–50, and 50–60 for Brand Value ($ billions). Prepare a frequency distribution for the data on Industry. Prepare a frequency distribution for the data on Brand Value ($ billions). TABLE 2.12 Data for 82 of the Most Valuable Brands Source: Data from Forbes, 2014. How has the crosstabulation helped in preparing the frequency distributions in parts (b) and (c)? What conclusions can you draw about the type of industry and the brand value? Revenue of World’s Most Valuable Brands. Refer to Table 2.12. 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). Prepare a frequency distribution for the data on Brand Revenue ($ billions). What conclusions can you draw about the type of industry and the brand revenue? 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 (%). Prepare a frequency distribution for the data on 1-Yr Value Change (%). What conclusions can you draw about the type of industry and the 1-year change in value? Car Fuel Efficiencies. The U.S. Department of Energys Fuel Economy Guide provides fuel efficiency data for cars and trucks (Fuel Economy website). A portion of the data from 2018 for 341 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 FuelData2018. a. Prepare a crosstabulation of the data on Size (rows) and Hwy MPG (columns). Use classes of 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, and 3034 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, and 3034 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. Develop a scatter diagram for the relationship between x and y. 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. Construct a side-by-side bar chart with x on the horizontal axis. 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.Driving Speed and Fuel Efficiency. A study on driving speed (miles per hour) and fuel efficiency (miles per gallon) for midsize automobiles resulted in the following data: 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.Low Temperatures and Snowfall. The file Snow contains temperature and snowfall data for 51 major U.S. cities over 30 years. For example, the average low temperature for Columbus, Ohio, is 44 degrees and the average annual snowfall is 27.5 inches. Construct a scatter diagram with the average annual low temperature on the horizontal axis and the average annual snowfall on the vertical axis. Does there appear to be any relationship between these two variables? Based on the scatter diagram, comment on any data points that seem to be unusual. Hypertension and Heart Disease. People often wait until middle age to worry about having a healthy heart. However, many studies have shown that earlier monitoring of risk factors such as blood pressure can be very beneficial (The Wall Street Journal). 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 individual’s blood pressure was measured to determine if they have hypertension. For the sample data, the following table shows the percentage of individuals with hypertension. 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. What does the display you developed in part (a) indicate about hypertension and age? Comment on differences by gender. Smartphone Ownership. Consider the following survey results that 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 10 years from now?Store Managers Time Study. 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?SAT Scores. The SAT is a standardized test used by many colleges and universities in their admission decisions. More than one million high school students take the SAT each year. 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: Show a frequency distribution and histogram. Begin with the first class starting at 800 and use a class width of 200. Comment on the shape of the distribution. What other observations can be made about the SAT scores based on the tabular and graphical summaries? Median Household Incomes. The file MedianHousehold contains the median household income for a family with two earners for each of the fifty states (American Community Survey). 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?State Populations. Data showing the population by state in millions of people follow (The World Almanac). Develop a frequency distribution, a percent frequency distribution, and a histogram. Use a class width of 2.5 million. Does there appear to be any skewness in the distribution? Explain. What observations can you make about the population of the 50 states? Startup Company Funds. According to the Wall Street Journal, 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. a. Construct a stem-and-leaf display. b. Comment on the display.Complaints Reported to BBB. Consumer complaints are frequently reported to the Better Business Bureau (BBB). Some industries against whom the most complaints are reported to the BBB are banks; cable and satellite television companies; collection agencies; cellular phone providers; and new car dealerships (USA Today). The results for a sample of 200 complaints are contained in the file BBB. Show the frequency and percent frequency of complaints by industry. Construct a bar chart of the percent frequency distribution. Which industry had the highest number of complaints? Comment on the percentage frequency distribution for complaints. Stock Price Volatility. 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 beta values for the stocks of the companies that make up the Dow Jones Industrial Average are shown in Table 2.17 (Yahoo Finance). 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?Education Level and Household Income. 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, https://www.census.gov/data/tables/time-series/demo/income-poverty/cps-hinc.html). TABLE 2.17 Betas for Dow Jones Industrial Average Companies 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: 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.Best Places to Work. Fortune magazine publishes an annual survey of the 100 best companies to work for. The data in the file FortuneBest 100 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). 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.53SE Colleges’ Year Founded and Percent Graduated. Refer to the data set in Table 2.18. Construct a crosstabulation with Year Founded as the row variable and % Graduate as the column variable. Use classes starling with 1600 and ending with 2000 in increments of 50 for Year Founded. For % Graduate, use classes starling with 35% and ending with 100% in increments of 5%. Compute the row percentages for your crosstabulation in part (a). Comment on any relationship between the variables. Colleges’ Year Founded and Cost. Refer to the data set in Table 2.18. Construct a scatter diagram to show the relationship between Year Founded and Tuition & Fees. Comment on any relationship between the variables. Colleges’ Cost and Percent Graduated. Refer to the data set in Table 2.18. Prepare a scatter diagram to show the relationship between Tuition & Fees and % Graduate. Comment on any relationship between the variables. Electric Vehicle Sales. Electric plug-in vehicle sales have been increasing worldwide. The table below displays data collected by the U.S. Department of Energy on electric plug-in vehicle sales in the words top markets in 2013 and 2015. (Data compiled by Argonne National Laboratory, U.S. Department of Energy website, https://www.energy.gov/eere/vehicles/fact-918-march-28-2016-global-plug-light-vehicle-sales-increased-about-80-2015) Construct a side-by-side bar chart with year as the variable on the horizontal axis. Comment on any trend in the display. Convert the above table to percentage allocation for each year. Construct a stacked bar chart with year as the variable on the horizontal axis. Is the display in part (a) or part (b) more insightful? Explain. Zoo Member Types and Attendance. 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: Construct a bar chart of total attendance over time. Comment on any trend in the data. Construct a side-by-side bar chart showing attendance by visitor category with year as the variable on the horizontal axis. Comment on what is happening to zoo attendance based on the charts from parts (a) and (b). 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 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.The movie industry is a competitive business. More than 50 studios produce hundreds of new movies for theater release each year, and the financial success of each movie 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 the movie was in release are common variables used to measure the success of a movie released to theaters. Data collected for the top 100 theater movies released in 2016 are contained in the file Movies2016 (Box Office Mojo website). Table 2.20 shows the data for the first 10 movies 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 movies that are released to theaters. 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.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. One of the first tasks of this new office is to review the previous year’s expenditures. The file QueenCity contains data on the previous year’s 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 city’s budget is being spent. Manageri al 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: Tables and/or graphical displays that show the amount of expenditures by category and percentage of total expenditures by category. 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.” 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.” Jon Weideman, first shift foreman for Cut-Rate Machining, Inc., is attempting to decide on a vendor from whom to purchase a drilling machine. He narrows his alternatives to four vendors: The Hole-Maker, Inc. (HM); Shafts & Slips, Inc. (SS); Judge’s Jigs (JJ); and Drill-for-Bits, Inc. (DB). Each of these vendors is offering machines of similar capabilities at similar prices, so the effectiveness of the machines is the only selection criteria that Mr. Weideman can use. He invites each vendor to ship one machine to his Richmond, Indiana manufacturing facility for a test. He starts all four machines at 8:00 a.m. and lets them warm up for two hours before starting to use any of the machines. After the warmup period, one of his employees will use each of the shipped machines to drill 3-centimeter-diameter holes in 25-centimeter-thick stainless-steel sheets for two hours. The widths of holes drilled with each machine are then measured and recorded. The results of Mr. Weideman’s data collection are shown in Table 2.22. Based on these results, from which vendor would you suggest Mr. Weideman purchase his new machine? Managerial Report Use graphical methods of descriptive statistics to investigate the effectiveness of each vendor. Include the following in your report: Scatter plots of the measured width of each hole (cm). Based on the scatter plots, a discussion of the effectiveness of each vendor and under which conditions (if any) that vendor would be acceptable. A discussion of possible sources of error in the approach taken to assess these vendors. 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. Compute the weighted mean. 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. 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. eICU Waiting Times. There is a severe shortage of critical care doctors and nurses to provide intensive-care services in hospitals. To offset this shortage, many hospitals, such as Emory Hospital in Atlanta, are using electronic intensive-care units (eICUs) to help provide this care to patients (Emory University News Center). eICUs use electronic monitoring tools and two-way communication through video and audio so that a centralized staff of specially trained doctors and nurseswho can be located as far away as Australiacan provide critical care services to patients located in remote hospitals without fully staffed ICUs. One of the most important metrics tracked by these eICUs is the time that a patient must wait for the first video interaction between the patient and the eICU staff. Consider the following sample of 40 patient waiting times until their first video interaction with the eICU staff. a. Compute the mean waiting time for these 40 patients. b. Compare the mean waiting time. c. Compute the mode. d. Compute the first and third quartiles.Middle-Level Manager Salaries. 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 salaries of middle-level managers across the nation. The following data show the salary, in thousands of dollars, for a sample of 15 middle-level managers employed at companies in the Atlanta area. Compute the median salary for the sample of 15 middle-level managers. Suppose the median salary of middle-level managers employed at companies located across the nation is $85,000. How does the median salary for middle-level managers in the Atlanta area compare to the median for managers across the nation? Compute the mean annual salary for managers in the Atlanta area and discuss how and why it differs from the median computed in part (a) for Atlanta area managers. Compute the first and third quartiles for the salaries of middle-level managers in the Atlanta area. Advertising Spending. 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). 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?Advertising Spending. 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). The top 12 companies and the amount each spent on advertising in billions of dollars are as follows. What is the mean amount spent on advertising? What is the median amount spent on advertising? What are the first and third quartiles? Time Spent Watching Traditional TV. Nielsen tracks the amount of time that people spend consuming media content across different platforms (digital, audio, television) in the United States. Nielsen has found that traditional television viewing habits vary based on the age of the consumer as an increasing number of people consume media through streaming devices (Nielsen website). The following data represent the weekly traditional TV viewing hours in 2016 for a sample of 14 people aged 18–34 and 12 people aged 35–49. Compute the mean and median weekly hours of traditional TV viewed by those aged 18–34. Compute the mean and median weekly hours of traditional TV viewed by those aged 35–49. Compare the mean and median viewing hours for each age group. Which group watches more traditional TV per week? Online Multiplayer Game Downloads. The creator of a new online multiplayer survival game has been tracking the monthly downloads of the newest game. The following table shows the monthly downloads (in thousands) for each month of the current and previous year. Compute the mean, median, and mode for number of downloads in the previous year. Compute the mean, median, and mode for number of downloads in the current year. Compute the first and third quartiles for downloads in the previous year. Compute the first and third quartiles for downloads in the current year. Compare the values calculated in parts a through d for the previous and current years. What does this tell you about the downloads of the game in the current year compared to the previous year? Automobile Fuel Efficiencies. 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.Unemployment Rates by State. The U.S. Bureau of Labor Statistics collects data on unemployment rates in each state. The data contained in the file UnemploymentRates show the unemployment rate for every state and the District of Columbia over two consecutive years. To compare unemployment rates for the previous year with unemployment rates for the current year, compute the first quartile, the median, and the third quartile for the previous year unemployment data and the current year unemployment data. What do these statistics suggest about the change in unemployment rates across the states over these two years? Motor Oil Prices. 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. Compute the average sales price per case for this product during the last quarter. Calculating Grade Point Averages. 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. Using the number of funds as weights, compute the weighted average total return for these mutual funds. 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? 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? Business School Ranking. 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.Revenue Growth Rate. Annual revenue for Corning Supplies grew by 5.5% in 2014, 1.1% in 2015, −3.5% in 2016, −1.1% in 2017, and 1.8% in 2018. What is the mean growth annual rate over this period? Mutual Fund Comparison. Suppose that at the beginning of Year 1 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?If an asset declines in value from $5000 to $3500 over nine years, what is the mean annual growth rate in the asset’s 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. Price of Unleaded Gasoline. 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). 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?Round-Trip Flight Prices. The following table displays round-trip flight prices from 14 major U.S. cities to Atlanta and Salt Lake City. 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? 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? Annual Sales Amounts. Varatta Enterprises sells industrial plumbing valves. The following table lists the annual sales amounts for the different salespeople in the organization for the most recent fiscal year. a. Compute the mean, variance, and standard deviation for these annual sales values. b. In the previous fiscal year, the average annual sales amount was 300,000 with a standard deviation of 95,000. Discuss any differences you observe between the annual sales amount in the most recent and previous fiscal years.Air Quality Index. 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?30E Cellular Phone Spending. According to the 2016 Consumer Expenditure Survey, Americans spend an average of $1124 on cellular phone service annually (U.S. Bureau of Labor Statistics website). Suppose that we wish to determine if there are differences in cellular phone expenditures by age group. Therefore, samples of 10 consumers were selected for three age groups (18–34, 35–44, 45 and older). The annual expenditure for each person in the sample is provided in the table below. Compute the mean, variance, and standard deviation for the each of these three samples. What observations can be made based on these data? Advertising Spend by Companies. 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. 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.Amateur Golfer Scores. Scores turned in by an amateur golfer at the Bonita Fairways Golf Course in Bonita Springs, Florida, during 2017 and 2018 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 2017 and 2018? What improvement, if any, can be seen in the 2018 scores?Consistency of Running Times. 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 coach’s 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.36E Consider a sample with a mean of 30 and a standard deviation of 5. Use Chebyshev’s theorem to determine the percentage of the data within each of the following ranges: 20 to 40 15 to 45 22 to 38 18 to 42 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. Use Chebyshev’s theorem to calculate the percentage of individuals who sleep between 4.5 and 9.3 hours. Use Chebyshev’s theorem to calculate the percentage of individuals who sleep between 3.9 and 9.9 hours. 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 Chebyshev’s theorem in part (a)? Price per Gallon of Gasoline. Suppose that the mean retail price per gallon of regular grade gasoline in the United States is 3.43 with a standard deviation of .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?GMAT Exam Scores. 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). Assume that GMAT scores are bell-shaped with a standard deviation of 100. What percentage of GMAT scores are 647 or higher? What percentage of GMAT scores are 747 or higher? What percentage of GMAT scores are between 447 and 547? 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. What is the z-score for a backyard structure costing $2300? What is the z-score for a backyard structure costing $4900? Interpret the z-scores in parts (a) and (b). Comment on whether either should be considered an outlier. If the cost for a backyard shed-office combination built in Albany, California, is $13,000, should this structure be considered an outlier? Explain. Best Places to Live. Each year Money magazine publishes a list of Best Places to Live in the United States. These listings are based on affordability, educational performance, convenience, safety, and livability. The list below shows the median household income of Money magazines top city in each U.S. state for 2017 (Money magazine website). a. Compute the mean and median for these household income data. b. Compare the mean and median values for these data. What does this indicate about the distribution of household income data? c. Compute the range and standard deviation for these household income data. d. Compute the first and third quartiles for these household income data. e. Are there any outliers in these data? What does this suggest about the data?NCAA Basketball Game Scores. 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 teams. 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.45E Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Provide the five-number summary for the data. Show the boxplot for the data in exercise 46. 46. Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Provide the five-number summary for the data.48E 49E Naples Half-Marathon Times. 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 the race results shown below 22 men and 31 women entered the 19–24 age class. Finish times in minutes are as follows. Times are shown in order of finish. 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? What is the median time for men and women runners? Compare men and women runners based on their median times. Provide a five-number summary for both the men and the women. Are there outliers in either group? Show the boxplots for the two groups. Did men or women have the most variation in finish times? Explain. Pharmaceutical Company Sales. Annual sales, in millions of dollars, for 21 pharmaceutical companies follow. Provide a five-number summary. Compute the lower and upper limits. Do the data contain any outliers? Johnson & Johnson’s 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? Show a boxplot. Cell Phone Companies Customer Satisfaction. Consumer Reports provides overall customer satisfaction scores for AT&T, 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 is used with 0 indicating completely dissatisfied and 100 indicating completely satisfied. Suppose that the ratings for the four cell-phone services in 20 metropolitan areas are as shown below. Consider T-Mobile first. What is the median rating? Develop a five-number summary for the T-Mobile service. Are there outliers for T-Mobile? Explain. Repeat parts (b) and (c) for the other three cell-phone services. Show the boxplots for the four cell-phone services on one graph. Discuss what a comparison of the boxplots tells about the four services. Which service does Consumer Reports recommend as being best in terms of overall customer satisfaction? Most Admired Companies. Fortune magazines list of the worlds most admired companies for 2014 is provided in the data contained in the file AdmiredCompanies (Fortune magazine website). The data in the column labeled 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 boxplot for the one-year total return.U.S. Border Crossings. 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 file 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). What are the mean and median numbers of crossings for these ports of entry? What are the first and third quartiles? Provide a five-number summary. Do the data contain any outliers? Show a boxplot. 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.Stock Price Comparison. The file StockComparison contains monthly adjusted stock prices for technology company Apple, Inc., and consumer-goods company Procter & Gamble (P&G) from 2013–2018. Develop a scatter diagram with Apple stock price on the horizontal axis and P&G stock price on the vertical axis. What appears to be the relationship between these two stock prices? Compute and interpret the sample covariance. Compute the sample correlation coefficient. What does this value indicate about the relationship between the stock price of Apple and the stock price of P&G? Driving Speed and Fuel Efficiency. A department of transportation’s study on driving speed and miles per gallon for midsize automobiles resulted in the following data: Compute and interpret the sample correlation coefficient. Smoke Detector Use and Death Rates. 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% as of 2015 (National Fire Protection Association website). With this increase in the use of home smoke detectors, what has happened to the death rate from home fires? The file 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.Stock Market Indexes Comparison. 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 file 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.Best Private Colleges. A random sample of 30 colleges from Kiplingers list of the best values in private college provided the data shown in the file BestPrivateColleges (Kiplinger website). 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 (%)?Americans Dining Out. Americans tend to dine out multiple times per week. The number of times a sample of 20 families dined out last week provides the following data. Compute the mean and median. Compute the first and third quartiles. Compute the range and interquartile range. Compute the variance and standard deviation. The skewness measure for these data is .34. Comment on the shape of this distribution. Is it the shape you would expect? Why or why not? Do the data contain outliers? NCAA Football Coaches Salaries. A 2017 USA Today article reports that NCAA football coaches’ salaries have continued to increase in recent years (USA Today). The annual base salaries for the previous head football coach and the new head football coach at 23 schools are given in the file Coaches. Determine the median annual salary for a previous head football coach and a new head football coach. Compute the range for salaries for both previous and new head football coaches. Compute the standard deviation for salaries for both previous and new head football coaches. 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. Physician Office Waiting Times. 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 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. 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?Worker Productivity and Insomnia. U.S. companies lose 63.2 billion per year from workers with insomnia. Accordign to a 2013 article in the Wall Street Journal, workers lose an average of 7.8 days of productivity per year due to lack of sleep. 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?Work Commuting Methods. 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 boxplot for each method. Does a comparison of the boxplots support your conclusion in part (c)?Household Incomes. The following data represent a sample of 14 household incomes ($1000s). Answer the following questions based on this sample. What is the median household income for these sample data? According to a previous survey, the median annual household income five years ago was $55,000. Based on the sample data above, estimate the percentage change in the median household income from five years ago to today. Compute the first and third quartiles. Provide a five-number summary. 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? 69SE Best Hotels. 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.NFL Teams Worth. In 2014, the 32 teams in the National Football League (NFL) were worth, on average, 1.17 billion, 5% more than in 2013. The following data show the annual revenue ( millions) and the estimated team value ( millions) for the 32 NFL teams in 2014 (Forbes website). 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?MLB Team Winning Percentages. 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.Money Market Funds Days to Maturity. 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. Automobile Speeds. 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. a. What is the mean speed of the automobiles traveling on this road? b. Compute the variance and the standard deviation.Annual Returns for Panama Railroad Company Stock. 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 provides annual returns for Panama Railroad stock from 1853 through 1880. 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, 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 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. Most of the variables shown in Table 3.9 are self-explanatory, but two of the variables require some clarification. ItemsThe total number of items purchased Net SalesThe 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.2CP 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.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, 2007, and 2012 (ElephantDatabase.org website). 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.1. 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? 2. 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.4. Consider the experiment of tossing a coin three times. Develop a tree diagram for the experiment. List the experimental outcomes. What is the probability for each experimental outcome? 5. 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?Code Churn. Code Churn is a common metric used to measure the efficiency and productivity of software engineers and computer programmers. It’s usually measured as the percentage of a programmer’s code that must be edited over a short period of time. Programmers with higher rates of code churn must rewrite code more often because of errors and inefficient programming techniques. The following table displays sample information for 10 computer programmers. Use the data in the table above and the relative frequency method to determine probabilities that a randomly selected line of code will need to be edited for each programmer. If you randomly select a line of code from Liwei, what is the probability that the line of code will require editing? If you randomly select a line of code from Sherae, what is the probability that the line of code will not require editing? Which programmer has the lowest probability of a randomly selected line of code requiring editing? Which programmer has the highest probability of a randomly selected line of code requiring editing? Tri-State Smokers. A Gallup Poll of U.S. adults indicated that Kentucky is the state with the highest percentage of smokers (Gallup website). Consider the following example data from the Tri-State region, an area that comprises northern Kentucky, southeastern Indiana, and southwestern Ohio. a. Use the data to compute the probability that an adult in the Tri-State region smokes. b. What is the probability of an adult in each state of the Tri-State region being a smoker? Which state in the Tri-State region has the lowest probability of an adult being a smoker?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 Powerball Lottery. The Powerball lottery is played twice each week in 44 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 69, and then select a Powerball number from the digits 1 through 26. To determine the winning numbers for each game, lottery officials draw 5 white balls out a drum of 69 white balls numbered 1 through 69 and 1 red ball out of a drum of 26 red balls numbered 1 through 26. 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 48192734 with a Powerball number of 10 provided the record jackpot of 1.586 billion (Powerball website). 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?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)?15. 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. List the sample points in the event an ace is selected. List the sample points in the event a club is selected. List the sample points in the event a face card (jack, queen, or king) is selected. 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?18. 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. What is the probability that the company selected has its corporate headquarters in California? What is the probability that the company selected has its corporate headquarters in California, New York, or Texas? What is the probability that the company selected has its corporate headquarters in one of the 8 states listed above? 19. 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. What is the probability that a respondent 18–29 years of age thinks that global warming will not pose a serious threat during his/her lifetime? 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? For a randomly selected respondent, what is the probability that a respondent answers yes? Based on the survey results, does there appear to be a difference between ages 18–29 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?Fatal Collisions with a Fixed Object. The National Highway Traffic Safety Administration (NHTSA) collects traffic safety-related data for the U.S. Department of Transportation. According to NHTSA’s data, 10,426 fatal collisions in 2016 were the result of collisions with fixed objects (NHTSA website, https://www.careforcrashvictims.com/wp-content/uploads/2018/07/Traffic-Safety-Facts-20l6_-Motor-Vehicle-Crash-Data-from-the-Fatality-Analysis-Reporting-System-FARS-and-the-General-Estimates-System-GES.pdf). The following table provides more information on these collisions. Assume that a collision will be randomly chosen from this population. What is the probability of a fatal collision with a pole or post? What is the probability of a fatal collision with a guardrail? What type of fixed object is least likely to be involved in a fatal collision? What is the probability associated with this type of fatal collision? What type of object is most likely to be involved in a fatal collision? What is the probability associated with this type of fatal collision? 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).23. 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} Find P(A), P(B), and P(C). Find A ∪ B and P(A ∪ B). Find A ∩ B and P(A ∩ B). Are events A and C mutually exclusive? 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?Americans Using Facebook and LinkedIn. A 2018 Pew Research Center survey (Pew Research website) examined the use of social media platforms in the United States. The survey found that there is a .68 probability that a randomly selected American will use Facebook and a .25 probability that a randomly selected American will use LinkedIn. In addition, there is a .22 probability that a randomly selected American will use both Facebook and LinkedIn. What is the probability that a randomly selected American will use Facebook or LinkedIn? What is the probability that a randomly selected American will not use either social media platform? 26. 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. What is the probability of selecting a Domestic Equity fund? What is the probability of selecting a fund with a 4-star or 5-star rating? 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? 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? Social Media Use. A marketing firm would like to test-market the name of a new energy drink targeted at 18- to 29-year-olds via social media. A study by the Pew Research Center found that 35% of U.S. adults (18 and older) do not use social media (Pew Research Center website, October 2015). The percentage of U.S. young adults age 30 and older is 78%. Suppose that the percentage of the U.S. adult population that is either age 1829 or uses social media is 67.2%. a. What is the probability that a randomly selected U.S. adult uses social media? b. What is the probability that a randomly selected U.S. adult is aged 1829? c. What is the probability that a randomly selected U.S. adult is 1829 and a user of social media?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?30. Suppose that we have two events, A and B, with P(A) = .50, P(B) = .60, and P(A ∩ B) = .40. Find P(A ∣ B). Find P(B ∣ A). Are A and B independent? Why or why not? 31. 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. What is P(A ∩ B)? What is P(A ∣ B)? 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. What general conclusion would you make about mutually exclusive and independent events given the results of this problem? Living with Family. Consider the following example survey results of 18- to 34-year-olds in the United States, in response to the question “Are you currently living with your family?” Develop the joint probability table for these data and use it to answer the following questions. What are the marginal probabilities? What is the probability of living with family given you are an 18- to 34-year-old man in the United States? What is the probability of living with family given you are an 18- to 34-year-old woman in the United States? What is the probability of an 18- to 34-year-old in the United States living with family? If, in the United States, 49.4% of 18- to 34-year-olds are male, do you consider this a good representative sample? Why? 33. 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. Develop a joint probability table for these data. Use the marginal probabilities of undergraduate major (business, engineering, or other) to comment on which undergraduate major produces the most potential MBA students. 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? 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? 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?35. 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?” Develop a joint probability table and use it to answer the following questions. Construct the marginal probabilities for Who Is better (I Am, My Spouse, We Are Equal). Comment. Given that the respondent is a husband, what is the probability that he feels he is better at getting deals than his wife? Given that the respondent is a wife, what is the probability that she feels she is better at getting deals than her husband? Given a response “My spouse” is better at getting deals, what is the probability that the response came from a husband? 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.Giving Up Electronics. A 2018 Pew Research Center survey found that more Americans believe they could give up their televisions than could give up their cell phones (Pew Research website). Assume that the following table represents the joint probabilities of Americans who could give up their television or cell phone. What is the probability that a person could give up her cell phone? What is the probability that a person who could give up her cell phone could also give up television? What is the probability that a person who could not give up her cell phone could give up television? Is the probability a person could give up television higher if the person could not give up a cell phone or if the person could give up a cell phone? 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).40. 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. Compute P(B ∩ A1), P(B ∩ A2), and P(B ∩ A3). Apply Bayes’ theorem, equation (4.19), to compute the posterior probability P(A2 ∣ B). Use the tabular approach to applying Bayes’ theorem to compute P(A1 ∣ B), P(A2 ∣ B), and P(A3 ∣ B). 41. A consulting firm submitted a bid for a large research project. The firm’s management initially felt they had a 50–50 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. What is the prior probability of the bid being successful (that is, prior to the request for additional information)? What is the conditional probability of a request for additional information given that the bid will ultimately be successful? 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?Prostate Cancer Screening. According to a 2018 article in Esquire magazine, approximately 70% of males over age 70 will develop cancerous cells in their prostate. Prostate cancer is second only to skin cancer as the most common form of cancer for males in the United States. One of the most common tests for the detection of prostate cancer is the prostate-specific antigen (PSA) test. However, this test is known to have a high false-positive rate (tests that come back positive for cancer when no cancer is present). Suppose there is a .02 probability that a male patient has prostate cancer before testing. The probability of a false-positive test is .75, and the probability of a false-negative (no indication of cancer when cancer is actually present) is .20. What is the probability that the male patient has prostate cancer if the PSA test comes back positive? What is the probability that the male patient has prostate cancer if the PSA test comes back negative? For older men, the prior probability of having cancer increases. Suppose that the prior probability of the male patient is .3 rather than .02. What is the probability that the male patient has prostate cancer if the PSA test comes back positive? What is the probability that the male patient has prostate cancer if the PSA test comes back negative? What can you infer about the PSA test from the results of parts (a), (b), and (c)? 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?Americans Without Health Insurance. The National Center for Health Statistics, housed within the U.S. Centers for Disease Control and Prevention (CDC), tracks the number of adults in the United States who have health insurance. According to this agency, the uninsured rates for Americans in 2018 are as follows: 5.1% of those under the age of 18, 12.4% of those ages 1864, and 1.l% of those 65 and older do not have health insurance (CDC website). Approximately 22.8% of Americans are under age 18, and 61.4% of Americans are ages 1864. a. What is the probability that a randomly selected person in the United States is 65 or older? b. Given that the person is an uninsured American, what is the probability that the person is 65 or older?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?47. A financial manager made two new investments—one 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. How many sample points exist for this experiment? Show a tree diagram and list the sample points. 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. List the sample points in the union of the events (O ∪ M). List the sample points in the intersection of the events (O ∩ M). Are events O and M mutually exclusive? Explain. 48. 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 Doesn’t Use Social Media and Other Websites to Voice Opinions About Television Programs Female 395 291 Male 323 355 What is the probability a respondent is female? What is the conditional probability a respondent uses social media and other websites to voice opinions about television programs given the respondent is female? 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?50. 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 What is the probability that a randomly selected viewer will rate the new show as average or better? 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?53. Refer again to the data from the MBA new-matriculants survey in exercise 52. Given that a person applied to more than one school, what is the probability that the person is 24–26 years old? 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? What is the probability that a person is 24–26 years old or applied to more than one school? 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? Is the number of schools applied to independent of age? Explain. 54. 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 18–29 .1485 .0604 30–49 .2273 .0907 50+ .4008 .0723 What is the probability a survey respondent will say she or he is not okay with this practice? Given a respondent is 30–49 years old, what is the probability the respondent will say she or he is okay with this practice? Given a respondent says she or he is not okay with this practice, what is the probability the respondent is 50+ years old? Is the attitude about this practice independent of the age of the respondent? Why or why not? Do attitudes toward this practice for respondents who are 18–29 years old and respondents who are 50+ years old differ? 55. 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. What is the probability of an individual’s 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)? Assume that individuals who do not purchase the company’s soap product buy from its competitors. What would be your estimate of the company’s market share? Would you expect that continuing the advertisement will increase the company’s market share? Why or why not? 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? 56. 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. 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. If B is defined as the event that the initial asking price is under $150,000, estimate the probability of B. What is the probability of A ∩ B? 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? 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?Robs Market (RM) is a regional food store chain in the southwest United States. David White, Director of Business Intelligence for RM, would like to initiate a study of the purchase behavior of customers who use the RM loyalty card (a card that customers scan at checkout to qualify for discounted prices). The use of the loyalty card allows RM to capture what is known as point-of-sale data, that is, a list of products purchased by customers as they check out of the market. David feels that better understanding of which products tend to be purchased together could lead to insights for better pricing and display strategies as well as a better understanding of sales and the potential impact of different levels of coupon discounts. This type of analysis is known as market basket analysis, as it is a study of what different customers have in their shopping baskets as they check out of the store. As a prototype study, David wants to investigate customer buying behavior with regard to bread, jelly, and peanut butter. RMs Information Technology (IT) group, at Davids request, has provided a data set of purchases by 1000 customers over a one-week period. The data set is in the file MarketBasket, and it contains the following variables for each customer: Breadwheat, white, or none Jellygrape, strawberry, or none Peanut buttercreamy, natural, or none The variables appear in the above order from left to right in the data set, where each row is a customer. For example, the first record of the data set is white grape none which means that customer 1 purchased white bread, grape jelly, and no peanut butter. The second record is white strawberry none which means that customer 2 purchased white bread, strawberry jelly, and no peanut butter. The sixth record in the data set is none none none which means that the sixth customer did not purchase bread, jelly, or peanut butter. Other records are interpreted in a similar fashion. David would like you to do an initial study of the data to get a better understanding of RM customer behavior with regard to these three products. Managerial Report Prepare a report that gives insight into the purchase behavior of customers who use the RM loyalty card. At a minimum your report should include estimates of the following: 1. The probability that a random customer does not purchase any of the three products (bread, jelly, or peanut butter). 2. The probability that a random customer purchases white bread. 3. The probability that a random customer purchases wheat bread. 4. The probability that a random customer purchases grape jelly given that he or she purchases white bread. 5. The probability that a random customer purchases strawberry jelly given that he or she purchases white bread. 6. The probability that a random customer purchases creamy peanut butter given that he or she purchases white bread. 7. The probability that a random customer purchases natural peanut butter given that he or she purchases white bread. 8. The probability that a random customer purchases creamy peanut butter given that he or she purchases wheat bread. 9. The probability that a random customer purchases natural peanut butter given that he or she purchases wheat bread. 10. The probability that a random customer purchases white bread, grape jelly, and creamy peanut butter.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?3. 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. Experimental outcomes are defined in terms of the results of the three interviews. List the experimental outcomes. Define a random variable that represents the number of offers made. Is the random variable continuous? Show the value of the random variable for each of the experimental outcomes. 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 7. The probability distribution for the random variable x follows. x f (x) 20 .20 25 .15 30 .25 35 .40 Is this probability distribution valid? Explain. What is the probability that x = 30? What is the probability that x is less than or equal to 25? What is the probability that x is greater than 30? 8. The following data were collected by counting the number of operating rooms in use at Tampa General Hospital over a 20-day period: On three of the days only one operating room 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 hospital’s operating rooms were used. Use the relative frequency approach to construct an empirical discrete probability distribution for the number of operating rooms in use on any given day. Draw a graph of the probability distribution. Show that your probability distribution satisfies the required conditions for a valid discrete 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?New Cable Subscribers. Spectrum provides cable television and Internet service to millions of customers. Suppose that the management of Spectrum subjectively assesses a probability distribution for the number of new subscribers next year in the state of New York as follows. a. Is this probability distribution valid? Explain. b. What is the probability Spectrum will obtain more than 400,000 new subscribers? c. What is the probability Spectrum 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?14. The following table is a partial probability distribution for the MRA Company’s projected profits (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 What is the proper value for f(200)? What is your interpretation of this value? What is the probability that MRA will be profitable? 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 .Golf Scores. During the summer of 2018, Coldstream Country Club in Cincinnati, Ohio, collected data on 443 rounds of golf played from its white tees. The data for each golfer’s score on the twelfth hole are contained in the DATAfile Coldstream12. Construct an empirical discrete probability distribution for the player scores on the twelfth hole. A par is the score that a good golfer is expected to get for the hole. For hole number 12, par is four. What is the probability of a player scoring less than or equal to par on hole number 12? What is the expected score for hole number 12? What is the variance for hole number 12? What is the standard deviation for hole number 12? 18. The American Housing Survey reported the following data on the number of times that owner-occupied and renter-occupied units had a water supply stoppage lasting 6 or more hours 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 Define a random variable x = number of times that owner-occupied units had a water supply stoppage lasting 6 or more hours in the past 3 months and develop a probability distribution for the random variable. (Let x = 4 represent 4 or more times.) Compute the expected value and variance for x. Define a random variable y = number of times that renter-occupied units had a water supply stoppage lasting 6 or more hours in the past 3 months and develop a probability distribution for the random variable. (Let y = 4 represent 4 or more times.) Compute the expected value and variance for y. What observations can you make from a comparison of the number of water supply stoppages reported by owner-occupied units versus renter-occupied units? New Tax Accounting Clients. New legislation passed in 2017 by the U.S. Congress changed tax laws that affect how many people file their taxes in 2018 and beyond. These tax law changes will likely lead many people to seek tax advice from their accountants (The New York Times). Backen and Hayes LLC is an accounting firm in New York state. The accounting firm believes that it may have to hire additional accountants to assist with the increased demand in tax advice for the upcoming tax season. Backen and Hayes LLC has developed the following probability distribution for x 5 number of new clients seeking tax advice. a. Is this a valid probability distribution? Explain. b. What is the probability that Backen and Hayes LLC will obtain 40 or more new clients? c. What is the probability that Backen and Hayes LLC will obtain fewer than 35 new clients? d. Compute the expected value, variance, and standard deviation 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.22. The demand for a product of Carolina Industries varies greatly from month to month. The probability distribution in the following table, based on the past two years of data, shows the company’s monthly demand. Unit Demand Probability 300 .20 400 .30 500 .35 600 .15 If the company bases monthly orders on the expected value of the monthly demand, what should Carolina’s monthly order quantity be for this product? Assume that each unit demanded generates $70 in revenue and that each unit ordered costs $50. How much will the company gain or lose in a month if it places an order based on your answer to part (a) and the actual demand for the item is 300 units? 23. In Gallup’s Annual Consumption Habits Poll, telephone interviews were conducted for a random sample of 1014 adults aged 18 and over. One of the questions was, “How many cups of coffee, if any, do you drink on an average day?” The following table shows the results 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. Develop a probability distribution for x. Compute the expected value of x. Compute the variance of x. 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 an average day. Compute the expected value of y and compare it to the expected value of x. 24. The J. R. Ryland Computer Company is considering a plant expansion to enable the company to begin production of a new computer product. The company’s 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, medium demand, 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 firm’s planners developed 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 Compute the expected value for the profit associated with the two expansion alternatives. Which decision is preferred for the objective of maximizing the expected profit? 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.32. Consider a binomial experiment with n = 10 and p = .10. Compute f(0). Compute f(2). Compute P(x ≤ 2). Compute P(x ≥ 1). Compute E(x). Compute Var(x) and σ. 33. Consider a binomial experiment with n = 20 and p = .70. Compute f(12). Compute f(16). Compute P(x ≥ 16). Compute P(x ≤ 15). Compute E(x). Compute Var (x) and σ. 34. For its Music 360 survey, Nielsen Co. asked teenagers and adults how each group has listened to music in the past 12 months. Nearly two-thirds of U.S. teenagers under the age of 18 say they use Google Inc.’s video-sharing site to listen to music and 35% of the teenagers said they use Pandora 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. Is randomly selecting 10 teenagers and asking whether or not they use Pandora Media Inc.’s online service a binomial experiment? What is the probability that none of the 10 teenagers use Pandora Media Inc.’s online radio service? What is the probability that 4 of the 10 teenagers use Pandora Media Inc.’s online radio service? What is the probability that at least 2 of the 10 teenagers use Pandora Media Inc.’s online 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?36. 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 are interested in the number of defective parts found. Describe the conditions under which this situation would be a binomial experiment. Draw a tree diagram similar to Figure 5.4 showing this problem as a two-trial experiment. How many experimental outcomes result in exactly one defect being found? Compute the probabilities associated with finding no defects, exactly one defect, and two defects. Americans Saving for Retirement. According to a 2018 survey by Bankrate.com, 20% of adults in the United States save nothing for retirement (CNBC website). Suppose that 15 adults in the United States are selected randomly. Is the selection of the 15 adults a binomial experiment? Explain. What is the probability that all of the selected adults save nothing for retirement? What is the probability that exactly five of the selected adults save nothing for retirement? What is the probability that at least one of the selected adults saves nothing for retirement? 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.42. A Gallup Poll showed that 30% of Americans are satisfied with the way things are going in the United States (Gallup website, September 12, 2012). Suppose a sample of 20 Americans is selected as part of a study of the state of the nation. Compute the probability that exactly 4 of the 20 Americans surveyed are satisfied with the way things are going in the United States. Compute the probability that at least 2 of the Americans surveyed are satisfied with the way things are going in the United States. For the sample of 20 Americans, compute the expected number of Americans who are satisfied with the way things are going in the United States. For the sample of 20 Americans, compute the variance and standard deviation of the number of Americans who are satisfied with the way things are going in the United States. Tracked Emails. According to a 2017 Wired magazine article, 40% of emails that are received are tracked using software that can tell the email sender when, where, and on what type of device the email was opened (Wired magazine website). Suppose we randomly select 50 received emails. What is the expected number of these emails that are tracked? What are the variance and standard deviation for the number of these emails that are tracked? 44. Consider a Poisson distribution with μ = 3. write the appropriate Poisson probability function. Compute f(2). Compute f(1). Compute P(x ≥ 2). 45. Consider a Poisson distribution with a mean of two occurrences per time period. Write the appropriate Poisson probability function. What is the expected number of occurrences in three time periods? Write the appropriate Poisson probability function to determine the probability of x occurrences in three time periods. Compute the probability of two occurrences in one time period. Compute the probability of six occurrences in three time periods. Compute the probability of five occurrences in two time periods. 46. Phone calls arrive at the rate of 48 per hour at the reservation desk for Regional Airways. Compute the probability of receiving three calls in a 5-minute interval of time. Compute the probability of receiving exactly 10 calls in 15 minutes. Suppose no calls are currently on hold. If the agent takes 5 minutes to complete the current call, how many callers do you expect to be waiting by that time? What is the probability that none will be waiting? If no calls are currently being processed, what is the probability that the agent can take 3 minutes for personal time without being interrupted by a call? 911 Calls. Emergency 911 calls to a small municipality in Idaho come in at the rate of one every 2 minutes. What is the expected number of 911 calls in one hour? What is the probability of three 911 calls in five minutes? What is the probability of no 911 calls in a five-minute period? Motor Vehicle Accidents in New York City. In a one-year period, New York City had a total of 11,232 motor vehicle accidents that occurred on Monday through Friday between the hours of 3 p.m. and 6 p.m. (New York State Department of Motor Vehicles website). This corresponds to mean of 14.4 accidents per hour. Compute the probability of no accidents in a 15-minute period. Compute the probability of at least one accident in a 15-minute period. 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.Emails Received. According to a 2017 survey conducted by the technology market research firm The Radicati Group, U.S. office workers receive an average of 121 emails per day (Entrepreneur magazine website). Assume the number of emails received per hour follows a Poisson distribution and that the average number of emails received per hour is five. a. What is the probability of receiving no emails during an hour? b. What is the probability of receiving at least three emails during an hour? c. What is the expected number of emails received during 15 minutes? d. What is the probability that no emails are received during 15 minutes?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 = 4.53. Suppose N = 15 and r = 4. What is the probability of x = 3 for n = 10? Online Holiday Shopping. More and more shoppers prefer to do their holiday shopping online from companies such as Amazon. Suppose we have a group of 10 shoppers; 7 prefer to do their holiday shopping online and 3 prefer to do their holiday shopping in stores. A random sample of 3 of these 10 shoppers is selected for a more in-depth study of how the economy has impacted their shopping behavior. What is the probability that exactly 2 prefer shopping online? What is the probability that the majority (either 2 or 3) prefer shopping online? 55E 56. Axline Computers manufactures personal computers at two plants, one in Texas and the other in Hawaii. The Texas plant has 40 employees; the Hawaii plant has 20. A random sample of 10 employees is to be asked to fill out a benefits questionnaire. What is the probability that none of the employees in the sample work at the plant in Hawaii? What is the probability that 1 of the employees in the sample works at the plant in Hawaii? What is the probability that 2 or more of the employees in the sample work at the plant in Hawaii? 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?58E 59. The U.S. Coast Guard (USCG) provides a wide variety of information on boating accidents including the wind condition at the time of the accident. The following table shows the results 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, and x = 4 for storm. Develop a probability distribution for x. Compute the expected value of x. Compute the variance and standard deviation for x. Comment on what your results imply about the wind conditions during boating accidents. 60. The Car Repair Ratings website provides consumer reviews and ratings for garages in the United States and Canada. The time customers wait for service to be completed is one of 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 Develop a probability distribution for x = wait-time rating. 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? 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 car dealerships, two were rated as providing outstanding wait-time service. Compare the likelihood of a new car dealership achieving an outstanding wait-time service rating as compared to other types of service providers. 61. 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 are unknown, the following respective probabilities are assigned: .3, .2, .25, .05, and .2. Show the probability distribution for the expense forecast. what is the expected value of the expense forecast for the coming year? 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 the financial position of the college. 62. A bookstore at the Hartsfield-Jackson Airport in Atlanta sells reading materials (paperback books, newspapers, magazines) as well as snacks (peanuts, pretzels, candy, etc.). A point-of-sale terminal collects a variety of information about customer purchases. Shown below is a table showing the number of snack items and the number of items of reading material 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 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 a randomly selected customer purchase. what is the probability of a customer purchase consisting of one item of reading materials and two snack items? what is the probability of a customer purchasing one snack item only? why is the probability f(x = 0, y = 0) = 0? Show the marginal probability distribution for the number of snack items purchased. Compute the expected value and variance. What is the expected value and variance for the number of reading materials purchased by a customer? 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 the relationship, if any, between the number of reading materials and number of snacks purchased 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?64. The Pew Research Center surveyed adults who own/use the following technologies: Internet, smartphone, email, and land-line phone (USA Today, March 26, 2014) and asked which of these technologies would be “very hard” to give up. The following responses were obtained: Internet 53%, smartphone 49%, email 36%, and land-line phone 28%. If 20 adult Internet users are surveyed, what is the probability that 3 users will report that it would be very hard to give it up? If 20 adults who own a land-line phone are surveyed, what is the probability that 5 or fewer will report that it would be very hard to give it up? If 2000 owners of smartphones were surveyed, what is the expected number that will report that it would be very hard to give it up? If 2000 users of email were surveyed, what is expected number that will report that it would be very hard to give it up? What is the variance and standard deviation? Investing in the Stock Market. According to a 2017 Gallup survey, the percentage of individuals in the United States who are invested in the stock market by age is as shown in the following table (Gallup website). Suppose Gallup wishes to complete a follow-up survey to find out more about the specific type of stocks people in the United States are purchasing. How many 18 to 29 year olds must be sampled to find at least 50 who invest in the stock market? How many people 65 years of age and older must be sampled to find at least 50 who invest in the stock market? If 1000 individuals are randomly sampled, what is the expected number of 18 to 29 year olds who invest in the stock market in this sample? What is the standard deviation of the number of 18 to 29 year olds who invest in the stock market? If 1000 individuals are randomly sampled, what is the expected number of those 65 and older who invest in the stock market in this sample? What is the standard deviation of the number of those 65 years of age and older who invest in the stock market? 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?67. PBS News Hour reported that 39.4% of Americans between the ages of 25 and 64 have at least a two-year college degree (PBS website, December 15, 2014). Assume that 50 Americans between the ages of 25 and 64 are selected randomly. What is the expected number of people with at least a two-year college-degree? What are the variance and standard deviation for the number of people with at least a two-year college degree? 68. Mahoney Custom Home Builders, Inc. of Canyon Lake, Texas, asked visitors to their website what is most important when choosing a home builder. Possible responses were quality, price, customer referral, years in business, and special features. Results showed that 23.5% of the respondents chose price as the most important factor (Mahoney Custom Homes website, November 13, 2012). Suppose a sample of 200 potential home buyers in the Canyon Lake area was selected. How many people would you expect to choose price as the most important factor when choosing a home builder? What is the standard deviation of the number of respondents who would choose price as the most important factor in selecting a home builder? What is the standard deviation of the number of respondents who do not list price as the most important factor in selecting a home builder? Arrivals to a Car Wash. Cars arrive at a car wash randomly and independently; the probability of an arrival is the same 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?70. A new automated production process averages 1.5 breakdowns per day. Because of the cost 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. What is 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?73. A deck of playing cards contains 52 cards, four of which are aces. What is the probability that the deal of a five-card hand provides A pair of aces? Exactly one ace? No aces? At least one ace? 74. U.S. News & World Report’s ranking of America’s best graduate schools of business showed 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 (America’s Best Graduate Schools, 2009 edition, U.S. News & World Report). Suppose that we randomly select 2 of the top 10 graduate schools of business. What is the probability that exactly one school has students with an average undergraduate GPA of 3.50 or higher? What is the probability that both schools have students with an average undergraduate GPA of 3.50 or higher? What is the probability that neither school has students with an average undergraduate GPA of 3.50 or higher? Great Grasslands Grains, Inc. (GGG) manufactures and sells a wide variety of breakfast cereals. GGG’s product development lab recently created a new cereal that consists of rice flakes and banana-flavored marshmallows. The company’s marketing research department has tested the new cereal extensively and has found that consumers are enthusiastic about the cereal when 16-ounce boxes contain at least 1.6 ounces and no more than 2.4 ounces of the banana-flavored marshmallows. As GGG prepares to begin producing and selling 16-ounce boxes of the new cereal, which it has named Go Bananas!, management is concerned about the amount of banana-flavored marshmallows. It wants to be careful not to include less than 1.6 ounces or more than 2.4 ounces of banana-flavored marshmallows in each 16-ounce box of Go Bananas! Tina Finkel, VP of Production for GGG, has suggested that the company measure the weight of banana-flavored marshmallows in a random sample of 25 boxes of Go Bananas! on a weekly basis. Each week, GGG can count the number of boxes out of the 25 boxes in the sample that contain less than 1.6 ounces or more than 2.4 ounces of banana- flavored marshmallows; if the number of boxes that fail to meet the standard weight of banana-flavored marshmallows is too high, production will be shut down and inspected. Ms. Finkel and her staff have designed the production process so that only 8% of all 16-ounce boxes of Go Bananas! fail to meet the standard weight of banana-flavored marshmallows. After much debate, GGG management has decided to shut down production of Go Bananas! if at least five boxes in a weekly sample fail to meet the standard weight of banana-flavored marshmallows. Managerial Report Prepare a managerial report that addresses the following issues. Calculate the probability that a weekly sample will result in a shutdown of production if the production process is working properly. Comment on GGG management’s policy for deciding when to shut down production of Go Bananas!. GGG management wants to shut down production of Go Bananas! no more than 1% of the time when the production process is working properly. Suggest the appropriate number of boxes in the weekly sample that must fail to meet the standard weight of banana-flavored marshmallows in order for production to be shut down if this goal is to be achieved. Ms. Finkel has suggested that if given sufficient resources, she could redesign the production process to reduce the percentage of 16-ounce boxes of Go Bananas! that fail to meet the standard weight of banana-flavored marshmallows when the process is working properly. To what level must Ms. Finkel reduce the percentage of 16-ounce boxes of Go Bananas! that fail to meet the standard weight of banana-flavored marshmallows when the process is working properly in order for her to reduce the probability at least five of the sampled boxes fail to meet the standard to .01 or less? Harriet McNeil, proprietor of McNeil’s Auto Mall, believes that it is good business for her atuomobile dealership to have more customers on the lot than can be served, as she believes this creates an impression that demand for the automobiles on her lot is high. However, she also understands that if there are far more customers on the lot than can be served by her salespeople, her dealership may lose sales to customers who become frustrated and leave without making a purchase. Ms. McNeil is primarily concerned about the staffing of salespeople on her lot on Saturday mornings (8:00 a.m. to noon), which are the busiest time of the week for McNeil’s Auto Mall. On Saturday mornings, an average of 6.8 customers arrive per hour. The customers arrive randomly at a constant rate throughout the morning, and a salesperson spends an average of one hour with a customer. Ms. McNeil’s experience has led her to conclude that if there are two more customers on her lot than can be served at any time on a Saturday morning, her automobile dealership achieves the optimal balance of creating an impression of high demand without losing too many customers who become frustrated and leave without making a purchase. Ms. McNeil now wants to determine how many salespeople she should have on her lot on Saturday mornings in order to achieve her goal of having two more customers on her lot than can be served at any time. She understands that occasionally the number of customers on her lot will exceed the number of salespersons by more than two, and she is willing to accept such an occurrence no more than 10% of the time. Managerial Report Ms. McNeil has asked you to determine the number of salespersons she should have on her lot on Saturday mornings in order to satisfy her criteria. In answering Ms. McNeil’s question, consider the following three quesitons: How is the number of customers who arrive in the lot on a Saturday morning distributed? Suppose Ms. McNeil currently uses five salespeople on her lot on Saturday morning. Using the probability distribution you identified in (1), what is the probability that the number of customers who arrive on her lot will exceed the number of salespersons by more than two? Does her current Saturday morning employment strategy satisfy her stated objective? Why or why not? What is the minimum number of salespeople Ms. McNeil should have on her lot on Saturday mornings to achieve her objective? Several years ago, management at Tuglar Corporation established a grievance committee composed of employees who volunteered to work toward the amicable resolution of disputes between Tuglar management and its employees. Each year management issue a call for volunteers to serve on the grievance committee, and 10 of the respondents are randomly selected to serve on the committee for the upcoming year. Employees in the Accounting Department are distressed because no member of their department has served on the Tuglar grievance committee in the past five years. Management has assured its employees in the Accounting Department that the selections have been made randomly, but these assurances have not quelled suspicions that management has intentionally omitted accountants from the committee. The table below summarizes the total number of volunteers and the number of employees from the Accounting Department who have volunteered for the grievance committee in each of the past five years: In its defense, management has provided these numbers to the Accounting Department. Given these numbers, is the lack of members of the Accounting Department on the grievance committee for the past five years suspicious (i.e., unlikely)? Managerial Report In addressing the issue of whether or not the committee selection process is random, consider the following questions: 1. How is the number of members of the Accounting Department who are selected to serve on the grievance committee distributed? 2. Using the probability distribution you identified in (1), what is the probability for each of these five years that no member of the Accounting Department has been selected to serve? 3. Using the probabilities you identified in (2), what is the probability that no member of the Accounting Department has been selected to serve during the past five years? 4. What is the cause of the lack of Accounting Department representation on the grievance committee over the past five years? What can be done to increase the probability that a member of the Accounting Department will be selected to serve on the grievance committee using the current selection method?

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