Skip to main content

Bartleby Sitemap - Textbook Solutions

All Textbook Solutions for Introduction to Business Statistics

A research firm observes that men are twice as likely as women to watch the Super Bowl on television. Does this information represent descriptive statistics or inferential statistics? Why?For each of the following, indicate whether the appropriate variable would be qualitative or quantitative. If you identify the variable as quantitative, indicate whether it would be discrete or continuous. a. Whether you own a Panasonic television set b. Your status as either a full-time or a part-time student c. The number of people who attended your school’s graduation last year d. The price of your most recent haircut e. Sam’s travel time from his dorm to the student union f. The number of students on campus who belong to a social fratenity or sorority What kinds of statistical data play a role in an auto insurance firm’s decision on the annual premium you’ll pay for your policy?For each of the following, indicate the scale of measurement that best describes the information. In 2008, Dell Corporation had approximately 78, 000 employees. USA Today reports that the previous day’s highest temperature in the United States was 105 degrees in Death Valley, California. An individual respondent answers “yes” when asked if TV contributes to violence in the United States. In a comparison test of family sedans, a magazine rates the Toyota Camry higher than the VW Passat.Most undergraduate business students will not go on to become actual practitioners of statistical research and analysis. considering this fact, why should such individuals bother to become familiar with business statistics?Bill scored 1200 on the Scholastic Aptitude Test and entered college as a physics major. As a freshman, he changed to business because he thought it was more interesting. Because he made the dean’s list last semester, his parents gave him $30 to buy a new Casio calculator. For this situation, identify at least one piece of information in the a. nominal scale of measurement. b. ordinal scale of measurement. c. interval scale of measurement. d. ratio scale of measurement.Roger Amster teaches an English course in which 40 students are enrolled. After yesterday’s class, Roger questioned the 5 students who always sit in the back of the classroom. Three of the 5 said “yes” when asked if they would like A Tale of Two Cities as the next class reading assignment. a. Identify the population and the sample in this situation. b. Is this likely to be a representative sample? If not, why not?In studying the performance of the company’s stock investments over the past year, the research manager of a mutual fund company finds that only 43% of the stocks returned more than the rate that had been expected at the beginning of the year. a. Could this information be viewed as representing the nominal scale of measurement? If so, explain your reasoning. If not, why not? b. Could this information be viewed as representing the ratio scale of measurement? If so, explain your reasoning. If not, why not?What was the primary use of statistics in ancient times?what ways can business statistics be useful in today’s business environment?What is the difference between descriptive statistics and inferential statistics? Which branch is involved when a state senator surveys some of her constituents in order to obtain guidance on how she should vote on a piece of legislation?In 2008, Piedmont Natural Gas Corporation sold 50.4 million cubic feet of gas to residential customers, an increase of 3.7% over the previous year. Does this information represent descriptive statistics or inferential statistics? Why? Source: Piedmont Natural Gas Corporation, Annual Report 2008. p. 16.An article in a fitness magazine described a study that compared the cardiovascular responses of 20 adult subjects for exercises on a treadmill, on a mini- trampoline, and jogging in place on a carpeted surface. Researchers found average heart rates were significantly less on the minitrampoline than for the treadmill and stationary jogging. Does this information represent descriptive statistics or inferential statistics? Why?What is the difference between a qualitative vairable and a quantitative variable? When would each be appropriate?What is the difference between discrete and continuous variable? Under what circumstances would each be applicable?The Acme School of Locksmithing has been accredited for the past 15 years. Discuss how this information might be interpreted as a a. qualitative variable. b. quantitative variable.Jeff Rowlen, a labor relations expert, has collected information on strikes in various industries. a. Jeff says, “Industry A has been harder hit by strikes than Industry B.” In what scale of measurement is this information? Why? b. Industry C has lost 10.8 days per worker, while Industry D has lost 14.5 days per worker. In what scale of measurement is this information? Why?The Snowbird Ski Lodge attracts skiers from several New England states. For each of the following scales of measurement, provide one example of information that might be relevant to the lodge’s business. a. Nominal b. Ordinal c. Interval d. Ratio Restaurants sometimes provide “customer reaction” cards so that customers can evaluate their dining experience at the establishment. What kinds of decisions might be made on the basis of this information?What kinds of statistical data might a burglar alarm company employ in trying to convince urban homeowners to purchase its product?The text claims that a company or organization might actually benefit when one of its employees uses statistics incorrectly. How can this be?The headline of an article in your daily newspaper begins “Research Study Reveals. . . . “As a statistics student who wishes to avoid accepting biased results, what single question should be foremost in your mind as you begin reading the article?The breakdown of U.S. cities having a population of at least 10,000 persons has been reported as follows. Source: Bureau of the Census, Statistical Abstract of the United States 2009, p.34. a. How many cities have a population of a least 25,000 but less than 500,000? b. How many cities have a population less than 2.50,000? c. How many cities have a population of at least 100,000 but less than 1,000,000? What percentage of cities are in this group? d. What is the class mark for the 100,000—under 250,000 class? e. Convert the table to a relative frequency distribution.The National Oceanic and Atmospheric Administration reports the following record high temperatures (degrees Fahrenheit) in 50 U.S. cities. These data are also provided in the file XR02056. Source: Bureau of the Census, Statistiacal Abstract of the United States 2009, p. 229. a. Construct a stem-and-leaf display for these data. b. Construct a frequency distribution. c. Determine the interval width and the class mark for each of the classes in your frequency distribution. d. Based on the frequency distribution obtained in part (b), draw a histogram and a relative frequency polygon to describe the data.2.57CE 2.58CE 2.59CE 2.60CE The following stem-and-leaf output has been generated by Minitab. The data consist of three-digit integers. From this display, is it possible to determine the exact values in the original data? If so, list the data values. If not, provide a set of data that could have led to this display. Interpret the numbers in the leftmost column of the output.For the period 2001—2008, the lristol-Myers Squibb Company, Inc. reported the following amounts (in billions of dollars) for (1) net sales and (2) advertising and product promouon. The data are also in the tile XR02062. Source: Bristol-Myers Squibb Company, Annual Reports, 2005, 2008. For these data, construct a line graph that shows both net sales and expenditures for advertising/product promotion over time. Some would suggest that increases in advertising should be accompanied by increases in sales. Does your line graph support this?2.63CE 2.64CE 2.65CE 2.66CE 2.67CE 2.68CE 2.69CE 2.70CE Using 10-yard intervals beginning with 200.0—under 210.0, 210.0—under 220.0, on up to 290.0—under 300.0, construct a frequency distribution for the distances traveled by the new ball.Using the same intervals as in part 1, construct a frequency distribution for the distances traveled by the conventional ball.1.3IC What is a frequency distribution? What benefits does it offer in the summarization and reporting of data values?2.2E The National Safety Council reports the following age breakdown for licensed drivers in the United State. Source: Bureau of the Census, Statistical Abstract of the United States 2009, p. 682. Identify the following for the 35-under 45 class: (a) frequency, (b) upper and lower limits, (c) width, and (d) midpoint.2.4E 2.5E Using the frequency distribution in Exercisc 2.5, identify the following for the 15—under 25 class: (a) frequency, (b) upper and lower limits, (c) width, and (d) midpoint.What is meant by the statement that the set of classes in a frequency distribution must be mutually exclusive and exhaustive?For commercial banks in each state, the U.S. Federal Deposit Insurance Corporation has listed their total deposits (billions of dollars) as follows. Source: Bureau of the Census, Statiscal Abstract of the United States 2009, p. 722. Construct a frequency distribution and a histogram for these data.The accompanying data describe the hourly wage rates (dollars per hour) for 30 employees of an electronics firm: 22.66 24.39 17.31 21.02 21.61 20.97 18.58 16.61 19.74 21.57 20.56 22.16 20.16 18.97 22.64 19.62 22.05 22.03 17.09 24.60 23.82 17.80 16.28 19.34 22.22 19.49 22.27 18.20 19.29 20.43 Construct a frequency distribution and a histogram for these data.The following performance scores have been recorded for 25 job applicants who have taken a pre-employment aptitude test administered by the company to which they applied: 66.6 75.4 66.7 59.2 78.5 80.8 79.9 87.0 941 70.2 92.8 86.9 92.8 66.8 65.3 100.8 76.2 87.8 71.0 92.9 97.3 82.5 78.5 72.0 76.2 Construct a frequency distribution and a histogram for these data.During his career in the NHL, hockey great Wayne Gretzky had the following season-total goals for each of his 20 seasons. 51 55 92 71 87 73 52 62 40 5.4 40 41 31 16 38 11 23 25 23 9 Construct a frequency distribution and a histogram for these data.According to the U.S. Department of Agriculture, the distribution of U.S. farms according to value of annual sales is as follows. Convert this information to a a. Relative frequency distribution. b. Cumulative frequency distribution showing “less than or within” frequencies.Convert the distribution in Exercise 2.3 to a Relative frequencydistribution. Cumulative frequency distribution showing “less than or within” frequencies.2.14E Using the frequency distribution obtained in Exercise 2.8, convert the information to a “less-than” ogive.For the frequency distribution constructed in Exercise 2.11, convert the information to a “less-than” ogive.(DATA SET) Note: Exercises 2.17-2.19 require a computer and statistical software.2.17E 2.18E 2.19E Construct a stem-and-leaf display for the following data 15 64 15 34 75 24 81 67 19 25 48 57 69 62 41 46 35 27 72 64 48 51 77 71 21 20 26 42 83 38 2.21E In the following stem-and-leaf display for a set of two-digit integers, the stem is the 10’s digit, and each leaf is the 1’s digit. What is the original set of data? 2|0022783|0113594|13445|47 2.23E 2.24E 2.25E 2.26E 2.28E What is the difference between a histogram and a bar chart? For what type of data would each be appropriate?2.30E 2.31E 2.32E 2.33E 2.34E It has been estimated that 92.9% of U.S. households own a telephone and that 68.5% have cable television. a. Why can’t this information be summarized in one pie chart? b. Construct two separate pie charts to summarize telephone ownership and cable television service.2.37E What is a scatterplot, and for what kind of data is it a useful descriptive device?2.39E 2.40E 2.41E For six local offices of a large tax prepartion firm, the following data describe x= revenues and y= expenses for supplies, freight, and postage during the previous tax preparation season: Draw a scatter diagram representing these data. Using the “eyeball” method, fit a straight line to the data. Does there appear to be any relationship between the variable? If so, is the relationship direct or inverse?In the 2009 stress tests applied to the nation’s biggest banks, the U.S. government determined that 10 of them needed a greater cushion of capital in order to absorb losses in a worst-case economic scenario. The banks, the bailout they received, and the additional cushion they were deemed to need are as shown below. Source: Bank Stress-Test Results, USA Today, May 8. 2009. p. 3B. a. Draw a scatter diagram representing these data. b. Using the “eyeball” method, fit a straight line to the data. c. Does there appear to be any relationship between the variables? If so, is the relationship direct or inverse? (DATA SET) Note: Exercises 2.44 and 2.45 require a computer and statistical software.2.44E 2.45E 2.46E Difference between simple tabulation and crosstabulation, and given a real or hypothetical example of each. Note: Exercises 2.48-2.50 can be done by hand, but computer statistical software is prefereable, if available.2.48E For the fleet described in Exercise 2.48, a. Construct a simple tabulation in which the counts are according to the type of engine. b. Construct a cross-tabulation describing the fleet, using type of engine and whether the vehicle has air conditioning as the categorization variables. c. Construct a display showing the average mpg according to type of engine and whether the vehicle has air conditioning. Do the categorization variables seem to be related to mpg? If so, how?2.50E 2.51E 2.52E 2.53E 2.54E The first seven ustomers of the day at a small donut shop have checks of $1.25, $2.36, $2.50, $2.I5, $4.55, $1.10, and $0.95, respetivcly. Based on thenumber of customers served each day, the manager of the shop claims that the shop needs an average check of $1.75 per pern to stay profItable. Given her contention, has the shop made a profit in serving the first seven customers?A dental supplies distributor ships a customer 50 boxes of product A, 30 boxes of R, 60 boxes of C, and 20 boxes of D. The unit shipping costs (dollars per box) for the four products are $5, $2, $4, and $10, respectively. What is the weighted mean for shipping cost per unit?The 2007 top-grossing feature film was Spiderman 3, a product that brought in $336.5 million at the box office. The gross receipts for this and the rest of the top- 20 feature films of that year are shown below. Determine the mean and median for these data. Is there a mode? If so, what is its numerical value? n N.v Yk Times Akariac2IL9, p. 413. $336.5 $322.7 $319.2 $309.4 $292.0 256.4 227.5 219.5 217.3 210.6 206.4 183.1 168.3 142.8 143.5 140.1 134.5 131.9 130.2 127.8 3.51CE 3.52CE 3.53CE 3.54CE 3.55CE 3.56CE A quality control supervisor has taken a sample of 16 bolts from the output of a thread-cutting machine and tested their tensile strengths. The results, in tons of force required for breakage, are as follows: 2.20 1.95 2.15 2.08 1.85 1.92 2.23 2.19 1.98 2.07 2.24 2.31 1.96 2.30 2.27 1.89 a. Determine the mean, median, range, and midrange. b. Calculate the mean absolute deviation. c. Calculate the standard deviation and variance.3.58CE 3.59CE A law enforcement agency, administering breathalyzer tests to a sample of drivers stopped at a New Year’s Eve roadblock, measured the following blood alcohol levels for the 25 drivers who were stopped: 0.00%0.08%0.15%0.18%0.02% 0.040.000.030.110.17 0.050.210.010.100.19 0.000.090.050.030.00 0.030.000.160.040.10 a. Calculate the mean and standard deviation for this sample. b. Use Chebyshev’s theorem to determine the minimum percentage of observations that should fall within k = 1.50 standard deviation units of the mean. Do the sample results support the theorem? c. Calculate the coefficient of variation for these data.3.61CE 3.62CE 3.63CE 3.64CE According to the Energy Information Administration, the average U.S. household spends $1196 per year for electricity. Assume that this finding could have been based on the electricity expenditures reported by 250 households, with the data in file XR03065. Source: eia.doe.gov, June 26, 2009. a. Confirm the mean and determine the median and the standard deviation of the electricity expenditures. b. Generate and interpret the box-and-whisker plot for the households from this region. c. From the results in parts (a) and (b), do there appear to be any “outlier” households? If so, for what reason(s) might energy-conservation officials wish to examine the habits or characteristics of these households?Bride’s magazine reports the cost of the average honeymoon as $5111. Assume that their findings could have been based on the honeymoon expenditures of a sample consisting of 300 couples whose costs are listed in data file XR03066. Source: msnbc.msn.com, itne 26. 2009. a. Confirm the mean and determine the median and the standard deviation of the honeymoon expenditures for this sample. b. Generate and interpret the box-and-whisker plot for the couples in the sample. c. From the results in parts (a) and (b), do there appear to be any “outlier’ couples who have spent an unusually large amount of money on their honeymoon? If so, what kinds of companies or organizations might have an interest in finding out how to identify such couples before they’ve made their honeymoon plans?3.67CE 3.68CE 3.69CE Determine the mean and the median wage rate for the data in Exercise 2.9.3.2E Erika operates a website devoted to providing inform ation and support for persons who are interested in organic gardening. According to the hit counter that records daily visitors to her site, the numbers of visits during the past 20 days have been as follows: 65, 36, 52, 70, 37, 55, 63, 59, 68, 56, 63, 63, 43, 46, 73, 41, 47, 75, 75, and 54. Determine the mean and the median for these data. Is there a mode? If so, what is its value?A social scientist for a children’s advocacy organization has randomly selected 10 Saturday-morning television cartoon shows and carried out a content analysis in which he counts the number of incidents of verbal or physical violence in each. For the 10 cartoons examined,the counts were as follows: 27, 12, 16, 22, 15, 30, 14, 30, 11, and 21. Determine the mean and the median for these data. Is there a mode? If so, what is its value?3.5E The following is a list of closing prices for 15 of the stocks held by an institutional investor. What was the average closing price for this sample of stocks? The median closing price? $31.69 56.69 65.50 83.50 56.88 72.06 121.44 97.00 42.25 71.88 70.63 35.81 83.19 43.63 40.06 3.7E According to a utility company, utility plant expenditures per employee were approximately S50,845, S43,690, $47,098, $56,121, and S49,369 for the years 2005 through 2009. Employees at the end of each year numbered 4738, 4637, 4540, 4397, and 4026, respect ively. Using the annual number of employees as weights, what is the weighted mean for annual utility plant investm ent per employee during this period?3.9E An observer stands at an overpass and, for each motorcycle that passes below, records the value of x — the number of riders on the motorcycle. a. What value would you anticipate for the mode of her data? Why? b. Would you anticipate that the mean would be greater than or less than the mode? Why? c. Would you anticipate that the mean would be greater than or less than the median? Why?3.11E 3.12E 3.13E 3.14E 3.15E 3.16E 3.17E 3.18E 3.19E For a sample of 11 employers, the most recent hourly wage increases were 18, 30, 25, 5, 7, 2, 20, 12, 15, 55, and 40 cents per hour. For these sample data, determine: a. The mean, median, range, and midrange. b. The mean absolute deviation. c. The standard deviation and variance.According to the U.S. Invironrnental Protection Agency, a sample of 10 subcompact models shows the following estimated values for highway fuel economy (mpg): 40, 33, 32, 30, 27, 29, 27, 23, 21, and 10. For these sample data, determine: a. The mean, median, range, and midrange. b. The mean absolute deviation. c. The standard deviation and variance.For a sample of eight apartment buildings in Chicago, the percentage-occupancy rates during a recent month were as shown below: 50.0% 79.1 61.3 43.9 68.1 70.0 72.5 66.3 For these sample data, determine: a. The mean, median, range, and midrange. b. The mean absolute deviation. c. The standard deviation and variance.3.23E 3.24E 3.25E 3.26E Data file XR02028 shows the depths (in meters) that 80 water-resistant watches were able to withstand just before leakage. For the watches in this sample, determine and interpret the following: a. The mean, median, range, and midrange. b. The mean absolute deviation. c. The standard deviation and variance.3.28E According to Chebyshev’s theorem, what percentage of observations should fall a. within 2.5 standard deviations of the mean? b. within 3.0 standard deviations of the mean? c. within 5.0 standard deviations of the mean?3.30E 3.31E The manufacturer of an extended-life lighthulh claims the bulb has an average life of 12,000 hours, with a standard deviation of 500 hours. If the distribution is bell shaped and symmetrical, what is the approximate percentage of these bulbs that will last a. between 11,000 and 13,000 hours? b. over 12,500 hours? c. less than 11,000 hours? d. between 11,500 and 13,000 hours?For college-bound high school seniors from a certain midwestern city, math scores on the Scholastic Aptitude Test (SAT) averaged 480, with a standard deviation of 100. Assume that the distribution of math scores is bell shaped and symmetrical. a. What is the approximate percentage of scores that were between 380 and 580? b. What is the approximate percentage of scores that were above 680? c. Charlie scored 580 on the math portion of the SAT. What is the approximate percentage of students who scored lower than Charlie? d. Betty scored 680 on the math portion of the SAT. What is the approximate percentage of students who scored higher than Charlie but lower than Betty?For data set A, the mean is $1235, with a standard deviation oI $140. For data set B, the mean is 15.7 inches, with a standard deviation of 1.87 inches. Which of these two data sets has the greater relative dispersion?3.35E 3.36E 3.37E 3.38E 3.39E 3.40E 3.41E 3.42E For a set of data, r2 is 0.64 and the variables x and y are inversely related. What is the numerical value of r?3.44E 3.45E 3.46E 3.47E 4.50CE 4.51CE For each of the following report titles, indicate whether the study involved was exploratory, descriptive, causal, or predictive, and explain your reasoning. a. “The Popularity of Bowling as a Participant Sport in Ohio” b. “The effects of TV Violence on Crime in Small Towns” c. “A Preliminary Investigation of the Market for Pet Foods” d. “Family Vacationing in the 21st Century”4.53CE 4.54CE A mail survey of junior executives is designed to measure how much time they spend reading The Wall Street journal each day and how the)’ feel about the newspaper’s content and layout. Formulate one question of each of the following types that might be included in the questionnaire: (a) multiple-choice; (b) dichotomous; (c) open-ended.4.56CE 4.57CE 4.58CE 4.59CE 4.60CE 4.61CE 4.62CE 4.64CE 4.67CE 4.68CE 4.69CE To test the effectiveness of a new type of plastic handcuffs, a law enforcement agency puts the cuffs on a sample of 30 persons who belong to the local weightlifting club. None is able to break free from the cuffs. What type of sampling technique does this represent? Explain your reasoning.4.71CE A college of business has 20 faculty members in Accounting, 30 in Marketing, 20 in Management, 15 in Finance, and 15 in Information Systems. The dean of the college asks her secretary to arbitrarily select 4, 6, 4, 3, and 3 persons from the respective departments to serve on a faculty committee. Is this a probability sample or a nonprobability sample? What specific type of probability or nonprobability sample does this procedure represent?4.73CE 4.74CE What is the difference between primary data and secondary data? Between internal secondary data and external secondary data?A published article reports that 60% of U.S. households have cable television. The president of an electronics firm clips the item from the paper and files it under “Cable TV data.” Would this material be considered primary data or secondary data?A pharmaceutical finn’s annual report states that company sales of over-the-ounter medicines increased by 48.1 %. a. To the firm itself, would this information be primary data or secondary data? b. To a competitor, what type of information would this represent?4.4E 4.5E 4.6E 4.7E 4.8E 4.9E 4.10E 4.11E 4.12E 4.13E 4.14E 4.15E 4.16E 4.17E 4.18E What are secondary data? Differentiate between internal and external secondary data.4.20E 4.21E 4.22E 4.23E 4.24E 4.32E Differentiate between sampling error and nonsampling error.4.34E 4.35E 4.36E 4.37E Attendees at an industrial trade show are given the opportunity to fill out a card that entitles them to receive a free software package from the sponsoring firm. The cards are placed in a bin, and 30 winners will be drawn. Considering the 30 winners as a sample from all of the persons filling out such cards, is this a probability sample or a nonprohability sample? What specific type of probability or nonprobability sample does this procedure represent?4.39E 4.40E 4.41E 4.42E For each of the following situations, would you recommend a sample or a census? Explain your reasoning in each case. a. A purchasing agent has just received a shipment of shock-resistant watches and wants to find out approximately how far they can be dropped onto a concrete surface without breaking the crystal. b. General Mills wants to learn the age, gender, and income characteristics of persons who consume Checrios breakfast cereal. c. The producers of NBC’s Tonight Show want to find out what percentage of TV viewers recognize a photo of host Jay Leno. d. A small company wants to determine whether U.S. companies that manufacture nuclear submarines might be interested in a new technique for purifying air when such craft are submerged.4.44E 4.45E 4.46E 4.47E 4.48E 4.49E It has been estimated that the odds of being struck by lightning in a given year are 1 to 240,000. Using this information: Source: lightningtalks.com. July 27, 2006. a. Express the odds in terms of “odds against.” b. What is the probability that a randomly selected individual will be struck by lightning this year? c. What is the probability that the person in part (b) will be struck by lightning at least once during the next 20 years?A fast-food chain gives each customer a coupon, the surface of which can be scratched to reveal whether a prize will be received. The odds for winning $1000 per week for life are listed as 1 to 200,000,000, while the odds for winning a free hamburger are 1 to 15. Sheila is going to have lunch at and will receive one coupon during her visit. Determine the probability that she will win a. $1000 per week for life. b. a free hamburger. c. either the lifetime $ 1000/week or a free hamburger. d. both the lifetime $ 1000/week and a free hamburger.For the situation in Exercise 5.61, what is the probability that Sheila will visit the franchise a. 5 times without winning a free hamburger? b. 10 times without winning a free hamburger? c. 20 times without winning a free hamburger? d. 40 times without winning a free hamburger?The “daily number” of a state lottery is a 3-digit integer from 000 to 999. Sam buys a ticket for the number 333. What is the probability that he will win? Is the probability found in part (a) a classical, relative frequency, or subjective probability? Explain your answer. Shirley buys a ticket for the number 418 since it came up yesterday and she thinks it’s “hot”. Is there a flaw in her logic? Explain.The U.S. Bureau of Justice released the following probabilities for those arrested for committing various felony crimes in the United States. Allen has been arrested for burglary, Bill has been arrested for a weapons offense, and Charlie has been arrested on a public-disorder charge. Assuming these individuals are typical perpetrators and the decisions regarding their respective fates are unrelated, determine the probability that Source: U.S. Bureauof Justce. as reported in Sam Meddis, “Felony Arrests: Short Terms USA Today. Juary 18. 1988. p. a. Allen will be jailed for more than a year. b. either Allen or Bill (or both) will be convicted. c. none of the three will be jailed for more than a year. d. Allen and Bill will be convicted, but Charlie will be found innocent. e. none will be prosecuted.For the three perpetrators in Exercise 5.64, determine the number of possibilities in which a. just one person is convicted. b. exactly two of the three persons are convicted. c. all three persons are convicted.Dave has been arrested for arson and has been convicted. Edgar is currently being prosecuted for a drug offense. Applying the U.S. Bureau of Justice data in Exercise 5.64, determine the probability that a. Dave will spend more than a year in jail. b. Edgar will be convicted. c. Edgar will spend more than a year in jail.A firm has two computer systems available for processing telephone orders. At any given time, system A has a 10% chance of being “down, while system B has just a 5% chance of being “down.” The computer systems operate independently. For a typical telephone order, determine the probability that a. neither computer system will be operational. b. both computer systems will be operational. c. exactly one of the computer systems will be operational. d. the order can be processed without delay.An industrial hoist is being used in an emergency job where the weight exceeds the design limits of two of its components. For the amount of weight being lifted, the probability that the upper attachment hook will fail is 0.20. The probability that the lower hook will fail is 0.10. What is the probability that the hoisting job will be successfully completed?The following relative frequency distribution describes the household incomes for families living in a suburban community: a. For a randomly selected household, what is the probability that its annual income is less than $80,000? b. If a household is known to have an income of at least $20,000, what is the probability that its annual income is in the $60,000—under S80,000 category? c. Two households are randomly selected from those whose income is at least $40,000 per year. What is the probability that both of these households are in the $80,000 or more category?Collecting data on traffic accident fatalities, the National Highway Traffic Safety Administration has found that 58.7% of the victims have 0.0% blood akoh ol content (RAC), 5.8% of the victims have from 0.01 to 0.07% RAC, and 35.5% of the victims have at least 0.08% RAC. For a randomly selected victim: Source: Statistical Abstract of the Unted States 2009. p. 681. a. What is the probability that the victim’s BAC was at least 0.01%? b. Given that the victim had been drinking prior to the accident, what is the probability that this victim’s RAC was at least 0.08%?During fiscal 1995, Ashland Exploration drilled 7 wells in the United States and 3 in Nigeria. One of the wells in Nigeria was productive and 2 of the wells in the United States were productive. The remaining wells were dry. For a well selected at random from those drilled during fiscal 1995, determine the following probabilities: Source: Ashland Oil, Inc., 1995 Fiscal Year Operational Supplement. p. 20. a. P(drilled in the United States) b. P(drilled in the United States or dry) c. P(dry|drilled in Nigeria)Avis, Inc., has reported that its fleet consists of 200,000 vehicles. If the vehicles are independent in terms of accident incidence and each has a 0.99999 chance of making it through the year without being in a major accident, what is the probability that the entire fleet will avoid a major accident during the year? Source: Avis.com, July 27. 2006.Data from the Federal Bureau of Investigation show that 1 of every 184 motor vehicles was stolen during 2003. Applying this statistic to 5 motor vehicles randomly selected from the nations vehicle population: Source: Bureau of the Census, Statistical Abstract of the United States 2009, pp. 194, 711. a. What is the probability that none of the 5 motor vehicles will be stolen? b. What is the probability that all 5 motor vehicles will be stolen? c. How many possibilities exist in which 2 of the 5 motor vehicles are stolen?Of the participants in a corporate meeting. 20% have had Red Cross training in cardiopulmonary resusc itation (CPR). During a break in the session, one part icipant is randomly selected to go across the Street and pick up some hoagies from the local deli. A patron at the deli is stricken by a severe heart attack. His survival probability is just 0.40 if he does not receive immediate CPR, but will be 0.90 if CPR can be administered right away. The meeting participant and the stricken person are the only customers in the deli, and none of the employees knows CPR. a. Without additional information, what is the probability that the stricken patron will survive? b. Given that the stricken patron survives, what is the probability that the meeting participant knew how to administer CPR? c. Given that the stricken patron does not survive, what is the probability that the meeting participant knew how to administer CPR?Of the adults in Jefferson Count, 10% have had CPR training. For a randomly selected group of adults from this county, how large would the group have to be in order for the probability that at least one group member has had CPR training to be at least 0.90?Over the years, a realtor estimates that 50% of those who contact her about a listing end up allowing her to provide a guided tour of the property’, 20% of those who take a guided tour follow up with a request for more information about the property, and 2% of those who make the follow-up informational request actually end up making an offer on the property. The realtor has just taken a young couple on a guided tourof one of her listed properties. Based on the probability estimates provided above what is the probability that the young couple will actually make an offer on the property?5.77CE 5.78CE When a machine is properly calibrated, 0.5% of its output is defective, but when it is out of adjustment, 6% of the output is defective. The technician in charge of calibration can successfully calibrate the machine in 90% of his attempts. The technician has just made an attempt to calibrate the machine. a. What is the probability that the machine is in adjustment? b. The first unit produced after the calibration effort is found to be defective. Given this information, what is the probability that the machine is in adjustment?In examining borrower characteristics versus loan delinquency, a bank has collected the following information: (1) 15% of the borrowers who have been employed at their present job for less than 3 years are behind in their payments. (2) 5% of the borrowers who have been employed at their present job for at least 3 years are behind in their payments, and (3) 80% of the borrowers have been employed at their present job for at least 3 years. Given this information: a. What is the probability that a randomly selected loan account will be for a person in the same job for at least 3 years who is behind in making payments? b. What is the probability that a randomly selected loan account will be for a person in the same job for less than 3 years or who is behind in making payments? c. If a loan account is behind, what is the probability that the loan is for a person who has been in the same job for less than 3 years?5.81CE A corporate board of directors consisting of 15 persons is to form a subcommittee of 5 persons to examine an environmental issue currently facing the firm. How many different subcommittees are possible?5.83CE A test to compare the taste of 6 soft drinks is being arranged. Each participant will be given 3 of the soft drinks and asked to indicate which one tastes best. a. How many different possibilities exist for the set of soft drinks that a given participant will taste? b. If we consider the order in which the participant in part (a) tastes the 3 soft drinks, how many possibilities exist?A certain brand of bicycle lock requires that each of four adjacent wheels be rotated to exactly the correct position in order to open the lock and separate the chain to which it is attached. If each wheel is labeled with the digits 0 through 9, how many different possibilities are available to the manufacturer in “programming” the sequence of numbers for opening any given lock?The president of a computer manufacturing firm states that there is a 70% chance that industry shipments of notebook computers will double in the next 5 years. Is this a classical probability, a relative frequency probability, or a subjective probability?5.2E 5.3E 5.4E Regarding Exercise 5.4, how might an observer employ the law of large numbers to verify the classical probability that you identified?5.6E 5.7E 5.8E If the odds are 4:7 that an event will occur, what is the corresponding probability?A sample space includes the events A. B. and C. Draw a Venn diagram in which the three events are mutually exclusive.A sample space includes the events A, B, and C. Draw a Venn diagram in which events A and B are mutually exclusive but events B and C are not mutually exclusive.The following contingency table of frequencies is based on a 5-year study of fire fatalities in Maryland. For purposes of clarity, columns and rows arc identified by the letters A—C and D—G. respectively. Source: National Fire Protection Association. The 1984 Fire Aknanac, p. 151. For this table, identify any two events that are mutually exclusive. For this table, identify any two events that intersect.Using the table in Exercise 5.12, how many victims were in the category described by: a. (A and A’)? b. (C or F)? c. (A’ and G’)? d. (B or G’)?Using the table in Exercise 5.12, what is the probability that a randomly selected victim would have been at least 60 years old and have had a blood alcohol level of at least 0.10%?5.15E Using the table in Exercise 5.15, assume that one well has been selected at random from the 48,673. a. What is the probability that the well was drilled in North America and was dry? b. What is the probability that the well was drilled in South America and was not dry?The owner of a McDonald’s restaurant in France is considering the possibility of opening up a new franchise at the other end of her town. At the same time, the manager of the Pennsylvania Turnpike is deciding whether to recommend raising the speed limit by 10 miles per hour. Draw a single Venn diagram representing their possible decisions. Explain any assumptions you have made regarding mutual exclusivity of events.5.18E According to data from the U.S. Energy Information Administration, the 60.0 million U.S. households with personal computers were distributed as shown here with regard to geographic location and access to the Internet. The entries represent millions of households. What is the probability that a randomly selected computer household would be in the category described by (South or Midwest or Yes)? In the category (West and No)? Source: Bureau of the Census, Statistical Abstract of the United State 2006, p. 638.There are 100 males and 120 females in the graduating class of a local high school. Thirty-five percent of the graduating males are on school sports teams, as are 30% of the graduating females. A local businessperson is going to donate $1000 to the favorite charity of a randomly selected graduate. What is the probability that the graduate selected will be a male who is not a member of a sports team? What is the probability that the graduate will be either a female or a member of a sports team?A financial advisor frequently holds investment counseling workshops for persons who have responded to his direct mailings. The typical workshop has 10 attendees. In the past, the advisor has found that in 35% of the workshops, nobody signs up for the advanced class that is offered; in 30% of the workshops, one person signs up; in 25% of the workshops, two people sign up; and in 10% of the workshops, three or more people sign up. The advisor is holding a workshop tomorrow. What is the probability that at least two people will sign up for the advanced class? What is the probability that no more than one person will sign up? Draw a Venn diagram that includes the possible events and their relative frequencies for this situation.A survey of employees at a large company found the following relative frequencies for the one-way distances the had to travel to arrive at work: a. What is the probability that a randomly selected individual will have to travel 11 or more miles to work? b. What is the probability that a randomly selected individual will have to travel between 6 and 15 miles to work? c. Draw a Venn diagram that includes the relative frequency probabilities in the table. d. Using the letter identifications provided, calculate the following probabilities: P (A or B or E); P(A or F); P(A’ or B); P(A or B or C’).In 2008, McDonald’s had 31,967 restaurants systemwide. Of these, 21,328 were operated by franchisees, 6502 by the company, and 4137 by affiliates. What is the probability that a randomly selected McDonald’s restaurant is operated by either a franchisee or an affiliate?For three mutually exclusive events P(A)=0.3,P(B)=0.6,andP(AorBorC)=1.0. What is the value of P(A or C)?It has been reported that the 49,600 employees of United Airlines are distributed among the following corporate functions: Source: United Airlines. Fact Sheet 2008. For the sample space consisting of United employees: a. Draw a Venn diagram representing events A, B, C, D, and E. b. What is the value of P(A)? c. What is the value of P(A or B)? d. What is the value of P(A or D’)?In 2003, Intergy Corporation had 2,631,752 electricity customers. Of these, 86.0% were in the residential category (R); 11.8% were commercial (C); 1.6% were industrial (I); and 0.6% were government and municipal (G). Source: Energy Corporaton. 2003 Annual Report. a. Draw a Venn diagram representing events R, C, I, and G. b. What is the value of P(R)? c. What is the value of P(C or G)? d. What is the value of P(R or C’)?According to the Bureau of Labor Statistics, there are 777,000 men and 588,000 women in the life, physical, and social science occupations category; and 786,000 men and 204,000 women in the farming, fishing, and forestry occupations category. For these 2,355,000 individuals, what is the probability that a randomly selected individual will either be a male or be in the life, physical, and social sciences category? Source: Encyclopaedia Britannica Almanac 2006. p. 835.Using the information presented in the table in Exercise 5.12, calculate the following probabilities: a. P(A or D) b. P(B or F) c. P(C or G) d. P(B or C or G)Using the infomation presented in the table in Exercise 5.15, calculate the following probabilities: a. P(D or N) b. P(D’ or N’) c. P(D orN’) d. P(D’orN)What is the difference between a marginal probabilitiy and a joint probability?5.31E 5.32E It has been reported that 57% of U.S. households that rent do not have a dishwasher, while only 28% of homeowner households do not have a dishwasher. If one household is randomly selected from each ownership category, determine the probability that Source: Bureau of the Census. Statistical Abstract of the United States 2009. p. 601. a. neither household will have a dishwasher. b. both households will have a dishwasher. c. the renter household will have a dishwasher, but the homeowner household will not. d. the homeowner household will have a dishwasher, but the renter household will not.A fair coin is tossed three times. What is the probability that the sequence will be head, tails, heads?A kitchen appliance has 16 working parts, each of which has a 0.99 probability of lasting through the product’s warranty period. The parts operate independently, but if one or more malfunctions, the appliances’ill plot work. What is the probability that a randomly selected appliance will work satisfactorily throughout the warranty period?An optometry practitioner group has found that half of those who need vision correction are patients who require bifocal lenses. a. For a randomly selected group of three people who require vision correction, what is the probability that all three will require bifocals? What is the probability that none of the three will require bifocals? b. If the three individuals had all been selected from an organization consisting of retirees over age 65, do you believe the joint probabilities calculated in part (a) would still be accurate? If not, why not?Through April 30 of the 2009 filing season, 15.8% of all individual U.S. tax returns were prepared by H&R Block. Source: H&R Block, Inc., Fast Facts 2009. a. If two individuals are randomly selected from those filing tax returns during this period, what is the probability that both of their tax returns were prep ared by H&R Block? b. In part (a), what is the probability that neither return was prepared by H&R Block? c. In part (a), what is the probability that exactly one of the two returns was prepared by H&R Block?Of employed U.S. adults age 25 or older, 90.4% have completed high school, while 34.0% have comp leted college. For H = completed high school, C = completed college, and assuming that one must complete high school before completing college, construct a tree diagram to assist your calculation of the following probabilities for an employed U.S. adult: Source: Bureau of the Census, Statistical Abstract of the United States 2009, p. 146. a. P(H) b. P(C|H) c. P(H and C) d. P(H and C’)A taxi company in a small town has two cabs. Cab A stalls at a red light 25% of the time, while cab B stalls just 10% of the time. A driver randomly selects one of the cars for the first trip of the day. What is the probability that the engine will stall at the first red light the driver encounters?Using the table in Exercise 5.12, calculate the conditional probability of C given each of the age groups, or P(C|D), P(C|E), etc. Compare these probabilities and speculate as to which age groups seem more likely than others to have been (according to the legal definition at that time, 0.10% blood alcohol content) intoxicated at the time they were victims.Charlie has read a survey result that says 60% of the adults in his town consider Wendy’s hamburgers to taste good. Charlie drives into the local Wendy s and questions a young couple about to enter the restaurant. According to Charlie, there’s only a 0.36 (i.e., 0.6 x 0.6) probability that both of these people will say Wendy’s hamburgers taste good. Do you think Charlie is correct? Explain.5.42E Based on the information in Exercise 5.21, if the advisor has at least one person sign up for the advanced class, what is the probability that at least three people have signed up ?Based on the information in Exercise 5.22, if a person is known to travel a one-way distance of at least 11 miles to work, determine the probability that he or she drives at least 31 miles to work.For U.S. live births, P(boy) and P(girl) are approximately 0.51 and 0.49, respectively.a According to a newspaper article, a medical process could alter the probabilities that a boy or a girl will be born. Researchers using the process claim that couples who wanted a boy were successful 85% of the time, while couples who wanted a girl were successful 77% of the time.b Assuming that the medical process does have an effect on the sex of the child: aSource: Bureau of the Census, Statistical Abstract of the United States 2009. P.Steve Twedt, Boy-Girl Selection Available Soon Here, Pittsburgh Press, December 31. 1987. pp. 1. 10. a. Without medical intervention, what is the probability of having a boy? b. With medical intervention, what is the conditional probability that a couple who wants a boy will have a boy? c. With medical intervention, what is the conditional probability that a couple who wants a girl will have a girl?Using the information in Exercise 5.45, assume that a couple who wanted a girl was randomly placed into either the treatment group (receiving the medical process described) or the control group (no treatment administered) in a test involving the medical procedure. a. What is the couple’s prior probability for being in the treatment group? b. The couple’s newborn child is a girl. Given this additional information, what is the revised probability that the couple was in the treatment groups A magician has two coins: One is unbalanced and lands heads 60% of the time; the other is fair and lands heads 50% of the time. A member of the audience randomly selects one of the coins and flips it. The result is heads. a. What is the prior probability that the fair coin was selected? b. Given additional information in the form of the single flip that came up heads, what is the revised probability that the coin is the fair one?For the information provided in Exercise 5.39, the cabbie finds that his car stalls at the first red light he encounters. Given this additional information, what is the probability that he has selected cab A?

Page: [1][2][3][4][5][6]