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business statistics a first course

Introduction To Business Statistics 7th Edition Ronald M. Weiers - Solutions

4.2 Using the bottom slider, change the standard deviation so that it is greater than 1. How does the shape of the red curve compare to that of the blue curve?
4.1 Position the top slider at the far left, then gradually move it to the far right. What effect does this have on the mean of the distribution?
7.83 In Exercise 7.82, the company would like to put in a greater weight “cushion” to help protect itself from consumer advocates. If the company wants to have just 2% of the packages contain less than 20 ounces, to what average weight must the filling machine be set?
7.77 The mileage death rate for motorcycle riders has been estimated to be about 39 deaths per 100 million miles of motorcycle travel. A national motorcycling association has 1200 members who travel a total of 2 million miles each year on their motorcycles. What is the probability that the next
7.73 Given the results of Exercise 7.72, evaluate the claim made by the public relations agency.
7.71 Of the 1.0 million persons of voting age in Maine, 72% voted in the 2008 presidential election. For a randomly selected group of 30 Maine residents who were of voting age at that time, what is the probability that at least 20 of these persons voted in the presidential election? Source:
7.70 For itemized tax returns in the $60,000–$75,000 income group for the most recent year reported, the average charitable contribution was $1935. Assume a normal distribution and a standard deviation of $400.Source: Statistical Abstract of the United States 2002, p. 360.a. For a randomly
7.69 During fiscal 2008, the average daily volume for FedEx Corporation was 7,000,000 packages per day.Assuming a normal distribution and a standard deviation of 800,000 packages per day, on what proportion of the days was the volume between 6,000,000 and 6,500,000 packages? Source: FedEx
7.67 It has been reported that the average monthly cell phone bill is $50. Assuming a normal distribution and a standard deviation of $10, what is the probability that a randomly selected cell phone subscriber’s bill last month was less than $35? More than $70? Source: Statistical Abstract of the
7.65 In Exercise 7.64, the maker of soft drink A claims its product to be “superior” to soft drink B. Given the results obtained in Exercise 7.64, do they appear to have a solid basis for their claim?
7.60 A computer statistical package has simulated 2000 random observations from a normal distribution with 5 80 and 5 20. Sketch the approximate box-andwhisker display for the resulting data.
7.59 A computer statistical package has simulated 1000 random observations from a normal distribution with 5 50 and 5 10. Sketch the approximate box-andwhisker display for the resulting data.
7.57 During 2008, U.S. general aviation pilots had 1.20 fatal crashes per 100,000 flying hours. Harriet Arnold is president of Arnold’s Flying Service, a company that operates a total of 50 sightseeing planes based in 20 regions of the United States. Altogether, the planes in this fleet are in
7.54 A random variable is Poisson distributed with 5 0.50 arrivals per minute. For the corresponding exponential distribution, and x 5 minutes until the next arrival, identify the mean of x and determine the following:a. P(x # 0.5)b. P(x # 1.5)c. P(x $ 2.5)d. P(x $ 3.0)
7.53 A random variable is Poisson distributed with l 5 0.02 occurrences per minute. For the corre sponding exponential distribution, and x 5 minutes until the next occurrence, identify the mean of x and determine the following:a. P(x $ 30.0)b. P(x $ 40.0)c. P(x $ 50.0)d. P(x $ 60.0)
7.52 A random variable is Poisson distributed with l 5 1.5 occurrences per hour. For the corresponding exponential distribution, and x 5 hours until the next occurrence, identify the mean of x and determine the following:a. P(x $ 0.5)b. P(x $ 1.0)c. P(x $ 1.5)d. P(x $ 2.0)
7.49 What is the relationship between the Poisson distribution and the exponential distribution?
7.46 The Electronic Industries Association reports that about 50% of U.S. households have a camcorder. For a randomly selected sample of 800 U.S. households, use the normal approximation to the binomial distribution in determining the probability that at least 410 of these households have a
7.45 Of all individual tax returns filed in the United States during the 2009 tax filing season, 15.8% were prepared by H&R Block. For a randomly selected sample of 900 tax returns filed during this period, use the normal approximation to the binomial distribution in determining the probability
7.44 About 40% of new single-family homes completed in the United States during 2007 were heated with electricity.For a randomly selected sample of 20 new singlefamily homes completed during that year and the discrete random variable, x 5 the number of homes in this group heated with electricity:
7.43 Approximately 80% of American families have some form of life insurance coverage. For a randomly selected sample of n 5 15 families, and the discrete random variable x 5 the number of families in the sample who are covered by life insurance: Source: American Council of Life Insurers, 2008 Life
In a certain binomial distribution, 5 0.30 and n 5 20. In using the normal approximation,a. What are the mean and standard deviation of the corresponding normal distribution?b. If x 5 the number of “successes” among the 20 observations, determine the following: P(x 5 5), P(4 # x # 7), P(1 # x
7.37 The KleerCo company in Exercise 7.36 would like to design a more durable pump so that no more than 2% of original-equipment pumps are returned under free warranty, and the standard deviation continues to be 10,000 miles. What will the new average service life have to be in order for the new
7.32 For the normal distribution described in Exercise 7.12, what tax preparation fee would have been exceeded by 90% of the tax preparation customers?
For the normal distribution described in Exercise 7.11, what first-mortgage amount would have been exceeded by only 5% of the mortgage customers?
For the normal distribution described in Exercise 7.15, what commuting time will be exceeded on only 10%of Jamal’s commuting days?
Using the standard normal table, find the following probabilities associated with z:a. P(21.96 # z # 1.27)b. P(0.29 # z # 1.00)c. P(22.87 # z # 21.22)
Using the standard normal table, find the following probabilities associated with z:a. P(20.36 # z # 0.00)b. P(z # 20.36)c. P(z $ 20.43)
A continuous random variable, x, is normally distributed with a mean of 200 grams and a standard deviation of 25 grams. Convert each of the following x values into its corresponding z-score:a. x 5 150b. x 5 180c. x 5 200d. x 5 285e. x 5 315
A continuous random variable, x, is normally distributed with a mean of $1000 and a standard deviation of $100. Convert each of the following x values into its corresponding z-score:a. x 5 $1000b. x 5 $750c. x 5 $1100d. x 5 $950e. x 5 $1225
7.15 On average, commuters in the Los Angeles, California, area require 30.0 minutes to get to work.Assume a normal distribution with a standard deviation of 5.0 minutes and a randomly selected Los Angeles-area commuter named Jamal. Source: The World Almanac and Book of Facts 2006, p. 474.a. What
7.14 The average American family of four spends $5000 per year on food prepared at home. Assuming a normal distribution with a standard deviation of $1000 and a randomly selected American family of four, what is the probability that the family’s annual spending for food prepared at home will be:
7.12 In 2009, the average charge for tax preparation by H&R Block, Inc. was $187. Assuming a normal distribution and a standard deviation of 5 $20, what proportion of H&R Block’s tax preparation fees were Source: hrblock.com, July 14, 2009.a. more than $187?b. between $147 and $227?c. between
7.10 The Canada Urban Transit Association has reported that the average revenue per passenger trip during a given year was $1.55. If we assume a normal distribution and a standard deviation of 5 $0.20, what proportion of passenger trips produced a revenue of Source: American Public Transit
7.9 If x is normally distributed with 5 25.0 and 5 5.0, determine the following:a. P(x $ 25.0)b. P(20.0 # x # 30.0)c. P(x # 30)d. P(x 5 26.2)e. P(15.0 # x # 25.0)f. P(x $ 15)
7.8 If x is normally distributed with 5 20.0 and 5 4.0, determine the following:a. P(x $ 20.0)b. P(16.0 # x # 24.0)c. P(x # 12)d. P(x 5 22.0)e. P(12.0 # x # 28.0)f. P(x $ 16)
7.7 Sketch two different normal distributions along a single x axis so that both of the following conditions are satisfied: (a) a 5 b and (b) a . b.
7.6 In the normal distribution, the probability that x will exceed ( 1 2) is the same as the probability that x will be less than ( 2 2). What characteristic of the normal distribution does this reflect?
7.5 It has been stated that the normal distribution is really a “family” of distributions. Explain.
7.4 What is the probability that a continuous random variable will take on any specific value? Explain your answer.
7.3 Why is the total area beneath a probability density function equal to 1.0?
7.1 What is the difference between a continuous probability distribution and a discrete probability distribution?
6.79 Use the computer in determining probabilities associated with the normal and exponential distributions.
6.79 Understand the nature and the applications of the exponential distribution, including its relationship to the Poisson distribution of Chapter 6.
6.80 J.D. Power and Associates’ Initial Quality Study reports that the industry-average problem rate for vehicles is 108 problems per 100 vehicles. The highestrated brand was Lexus, with a rate of just 84 problems per 100 vehicles. On the other hand, BMW’s Mini was reported as having 165
6.79 Use the standard normal distribution and z-scores to determine probabilities associated with the normal distribution.
6.79 Understand the nature and the applications of the normal distribution.
6.79 A tire manufacturer has advertised that only 2%of its tires have surface blemishes. Further, the manufacturer argues that tires with such blemishes are perfectly safe, and with only the physical appearance suffering very slightly. A consumer magazine randomly purchases 40 of the tires for an
6.78 It has been estimated that 5% of people who are hospitalized pick up infections while in the hospital, and that 2.2 million people a year get sick and 88,000 die because of these infections. Experts advise patients to be sure that health care personnel have washed their hands, to select
6.74 A gorilla once made headlines in 400 newspapers and appeared on three national television shows after correctly “selecting” the winner of 13 out of 20 football games. He had made his “choice” for each game by grabbing one of two pieces of paper on which the names of the teams were
6.72 According to the U.S. Centers for Disease Control and Prevention, Americans 85 years of age and older experience flu-associated respiratory and circulatory illness at an annual rate of approximately 1200 cases per 100,000 persons. If a rural county has 500 seniors in this age group, what is
6.71 The Bureau of Labor Statistics says that baggage handlers, trash haulers, and coal miners are among the occupations having the highest risk of a debilitating injury or illness. For coal miners working over the course of a year, the injury rate has been reported as 3.6 injuries per 100 coal
6.69 In 2004, 50% of all U.S. families had a net worth less than $93,000. What is the probability that exactly three of a randomly selected sample of five families would have a net worth less than $93,000? Source: Statistical Abstract of the United States 2009, p. 459.
6.68 A large plumbing contractor buys eight 200-foot rolls from the producer described in Exercise 6.67.Determine the probability that no more than three of the eight rolls will be flawless.
6.62 Unknown to a quality-control inspector, 20% of a very large shipment of electric switches are defective.The inspector has been told to reject the shipment if, in a sample of 15 switches, 2 or more are defective. What is the probability that the shipment will be rejected?6.63 Repeat Exercise
6.59 Twenty percent of the population of Maryland describe themselves as binge drinkers. For a randomly selected group of 5 Maryland residents, use the appropriate statistical table to describe the probability distribution for x 5 the number in the sample who describe themselves as binge drinkers.
6.58 During the 2009 tax filing season, 15.8% of all individual U.S. tax returns were prepared by H&R Block. For a random selection of 3 tax returns, describe the probability distribution for x 5 the number in the sample whose returns were prepared by H&R Block.Source: H&R Block, Inc., Fast Facts
6.57 In Exercise 6.56, suppose that three of the customers are interested in the same car, and that they will go elsewhere if it has already been sold. Would it be appropriate to use the binomial distribution under these conditions?Why or why not?
6.55 During 2007, the crash rate for commuter air carriers was 1.0 per 100,000 flying hours. Assuming this rate continues, what is the probability that there will be no more than one crash in the next 50,000 flying hours?Source: Statistical Abstract of the United States 2009, p. 662.
6.49 Taxicab drivers are more likely to be murdered on the job than members of any other occupation, even police officers and security guards. The annual murder rate for cab drivers is 30.0 homicides per 100,000 workers, compared to just 0.6 per 100,000 for all occupations. Assume that taxicab
6.48 The Federal Aviation Administration reports that American Airlines got 6.06 complaints of mishandled baggage per 1000 passengers in 2008. Assuming this rate applies to the next 500 passengers who depart from Portland, Oregon, on American Airlines flights, what is the probability that at least
6.47 According to the Mortgage Bankers Association of America, the foreclosure rate on home mortgages in 2007 was 2%. Assuming that this rate is applicable to a community where 500 homes have mortgages, use the Poisson approximation to the binomial distribution to determine the following for x 5
6.44 During the 12 p.m.–1 p.m. noon hour, arrivals at a curbside banking machine have been found to be Poisson distributed with a mean of 1.3 persons per minute. If x 5 number of arrivals during a given minute, determine the following:a. E(x)b. P(x 5 0)c. P(x 5 1)d. P(x # 2)e. P(1 # x # 3)
6.43 The U.S. divorce rate has been reported as 3.6 divorces per 1000 population. Assuming that this rate applies to a small community of just 500 people and is Poisson distributed, and that x 5 the number of divorces in this community during the coming year, determine the following: Source: New
6.42 Arrivals at a walk-in optometry department in a shopping mall have been found to be Poisson distributed with a mean of 2.5 potential customers arriving per hour. If x 5 number of arrivals during a given hour, determine the following:a. E(x)b. P(x 5 1)c. P(x 5 3)d. P(x # 5)e. P(2 # x # 6)
6.41 In 2006, there were about 490 motor vehicle thefts for every 100,000 registrations. Assuming (1) a Poisson distribution, (2) a community with a comparable theft rate and 1000 registered motor vehicles, and (3) x 5 the number of vehicles stolen during the year in that community, determine the
6.40 For a discrete random variable that is Poisson distributed with l 5 9.6, determine the following:a. P(x 5 7)b. P(x 5 9)c. P(x # 12)d. P(x $ 10)
6.39 For a discrete random variable that is Poisson distributed with l 5 2.0, determine the following:a. P(x 5 0)b. P(x 5 1)c. P(x # 3)d. P(x $ 2)
6.34 Using the hypergeometric distribution, with N 5 4, n 5 2, and s 5 3, determine the following:a. P(x 5 0)b. P(x 5 1)c. P(x 5 2)6.35 Using the hypergeometric distribution, with N 5 5, n 5 2, and s 5 3, determine the following:a. P(x 5 0)b. P(x 5 1)c. P(x 5 2)
6.33 Under what circumstances should the hypergeometric distribution be used instead of the binomial distribution?
6.32 Every day, artists at Arnold’s House of Fine Figurines produce 5 miniature statues that must be sanded and painted. Past experience has shown that 10%of the statues have a defect that does not show up until after the statue has been sanded and painted. Whenever a statue is found to have this
6.28 OfficeQuip is a small office supply firm that is currently bidding on furniture and office equipment contracts with four different potential customers who are of comparable size. For each contract, OfficeQuip would gain a profit of$50,000 if that contract were accepted, so the company could
6.26 The U.S. Department of Labor has reported that 30% of the 2.1 million mathematical and computer scientists in the United States are women. If 3 individuals are randomly selected from this occupational group, and x 5 the number of females, determine P(x 5 0), P(x 5 1), P(x 5 2), and P(x 5 3).
6.24 It has been reported that the overall graduation rate for football players at Division I-A colleges and universities is 65%. Source: “How Football Rates,” USA Today, December 20, 2005, p. 12C.a. If five players are randomly selected from the entire population of Division I-A football
6.22 According to the National Marine Manu fac turers Association, 50.0% of the population of Vermont were boating participants during the most recent year. For a randomly selected sample of 20 Vermont residents, with the discrete random variable x 5 the number in the sample who were boating
6.19 Twelve trials are conducted in a Bernoulli process in which the probability of success in a given trial is 0.3.If x 5 the number of successes, determine the following:a. E(x)b. xc. P(x 5 3)d. P(2 # x # 8)e. P(x . 3)
6.18 Seven trials are conducted in a Bernoulli process in which the probability of success in a given trial is 0.7.If x 5 the number of successes, determine the following:a. E(x)b. xc. P(x 5 3)d. P(3 # x # 5)e. P(x . 4)
6.17 When we are sampling without replacement, under what conditions can we assume that the constant p assumption has been satisfactorily met?
6.16 What is necessary for a process to be considered a Bernoulli process?
6.7 Determine the mean, variance, and standard deviation of the following discrete probability distribution:x 0 1 2 3 4 P(x) 0.10 0.30 0.30 0.20 0.10
6.6 Determine the mean, variance, and standard deviation of the following discrete probability distribution:x 0 1 2 P(x) 0.60 0.30 0.10
6.5 A discrete random variable can have the values x 5 3, x 5 8, or x 5 10, and the respective probabilities are 0.2, 0.7, and 0.1. Determine the mean, variance, and standard deviation of x.
6.1 Why is a random variable said to be “random”?
5.85 Use the appropriate probability distribution in determining the probability that a discrete random variable will have a given value or a value in a given range.
5.85 Understand what is meant by a Bernoulli process and how this applies to the consecutive trials associated with the binomial distribution.
5.85 Differentiate among the binomial, hypergeometric, and Poisson discrete probability distributions and their applications.
5.85 Determine whether the random variable in a probability distribution is of the discrete type or the continuous type.
5.85 Understand both the concept and the applications of a probability distribution for a random variable.
3.. If a student is randomly chosen from those who have defaulted on their computer payments, determine the revised probability that the student is from the “most likely to default” university identified in question 2.
2.. Repeat question 1 for each of the other universities. Do any of the conditional probabilities seem especially high or low compared to the others?In general, which school is associated with those most likely to default, and which school is associated with those least likely to default?
1.. Given that a student attended university number 1, determine the conditional probability that he or she defaulted on the computer payments.
5.85 In the Baldwin Computer Sales case, visited previously in Chapter 3, one of the areas of concern regarding the student purchase program was whether the probability of defaulting on the computer payments might be related to the university attended by the student. Using the BALDWIN data file,
5.85 Set up a contingency table for the appropriate variables, then determine the following probabilities:a. [variables 4 and 26] Given that the random respondent is a female, what is the probability that she spends at least $15 during a trip to Springdale Mall? Is a male more likely or less likely
5.85 Based on the relative frequencies for responses to each variable, determine the probability that a randomly selected respondenta. [variable 4] spends at least $15 during a trip to Springdale Mall.b. [variable 5] spends at least $15 during a trip to Downtown.c. [variable 6] spends at least $15
5.81 A security service employing 10 officers has been asked to provide 3 persons for crowd control at a local carnival. In how many different ways can the firm staff this event?
5.77 According to Sears, two-thirds of U.S. homeowners have an appliance from Sears. In a randomly selected group of three homeowners, what is the probability that all three would have an appliance from Sears? That at least one of the three would have an appliance from Sears?Source: Sears
5.73 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 nation’s vehicle population:Source: Bureau of the Census, Statistical Abstract of the United States 2009, pp.
5.72 Avis, Inc., has reported that its fleet consists of 200,000 vehicles. If the vehicles are indepen dent 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
5.70 Collecting data on traffic accident fatalities, the National Highway Traffic Safety Administration has found that 58.7% of the victims have 0.0% blood alcohol content (BAC), 5.8% of the victims have from 0.01 to 0.07% BAC, and 35.5% of the victims have at least 0.08% BAC. For a randomly
5.69 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,

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