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business statistics a first course
Introduction To Business Statistics 7th Edition Ronald M. Weiers - Solutions
5.64 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
5.63 The “daily number” of a state lottery is a 3-digit integer from 000 to 999.a. Sam buys a ticket for the number 333. What is the probability that he will win?b. Is the probability found in part (a) a classical, relative frequency, or subjective probability? Explain your answer.c. Shirley
5.62 For the situation in Exercise 5.61, what is the probability that Sheila will visit the franchisea. 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?
5.61 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
5.60 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
5.59 A sales representative has 35 customers throughout the state and is planning a trip during which 20 will be visited. In how many orders can the visits be made?
5.58 A roadside museum has 25 exhibits but enough space to display only 10 at a time. If the order of arrangement is considered, how many possibilities exist for the eventual display?
5.57 How many different combinations are possible if 6 substitute workers are available to fill 3 openings created by employees planning to take vacation leave next week?
5.56 An investment counselor would like to meet with 12 of his clients on Monday, but he has time for only 8 appointments. How many different combinations of the clients could be considered for inclusion into his limited schedule for that day?
5.48 A tax auditor has 9 different returns to audit, but will have time to examine only 5 of them tomorrow. In how many different orders can tomorrow’s task be carried out?
5.48 Bill has 6 textbooks, but can fit only 4 of them onto a small shelf. If the other 2 books have to sit on the desk, in how many ways can Bill arrange the shelf?
5.49 Machine A produces 3% defectives, machine B produces 5% defectives, and machine C produces 10%defectives. Of the total output from these machines, 60% of the items are from machine A, 30% from B, and 10% from C. One item is selected at random from a day’s production.a. What is the prior
5.48 For the information provided in Exercise 5.39, the cabbie finds that his car stalls at the first red light he encounters. Given this addi tional information, what is the probability that he has selected cab A?
5.47 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
5.46 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
5.45 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
5.44 A dryer manufacturer purchases heating elements from three different suppliers:Argostat, Bermrock, and Thermtek. Thirty percent of the heating elements are supplied by Argostat, 50% by Bermrock, and 20% by Thermtek. The elements are mixed in a supply bin prior to inspection and installation.
5.44 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.
5.43 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?
5.42 Based on the information in Exercise 5.20, if the student chosen is known to be on a sports team, what is the probability that the student is a female?
5.41 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 3 0.6) probability
5.40 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%
5.39 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
5.38 Of employed U.S. adults age 25 or older, 90.4%have completed high school, while 34.0% have completed college. For H 5 completed high school, C 5 completed college, and assuming that one must complete high school before completing college, construct a tree diagram to assist your calculation of
5.37 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
5.36 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
5.35 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 appliance will not work.What is the probability that a randomly selected appliance will work
5.34 A fair coin is tossed three times. What is the probability that the sequence will be heads, tails, heads?
5.33 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
5.32 If events A and B are independent, will P(A|B) be greater than, less than, or equal to P(A)? Explain.
5.31 It is possible to have a sample space in which P(A) 5 0.7, P(B) 5 0.6, and P(A and B) 5 0.35. Given this information, would events A and B be mutually exclusive?Would they be independent?
5.30 What is the difference between a marginal probability and a joint probability?
5.29 Using the information presented in the table in Exercise 5.15, calculate the following probabilities:a. P(D or N)b. P(D9 or N9)c. P(D or N9)d. P(D9 or N)
5.28 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)
5.27 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
5.26 In 2003, Entergy 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: Entergy Corporation, 2003 Annual Report.a. Draw a Venn diagram
5.25 It has been reported that the 49,600 employees of United Airlines are distributed among the following corporate functions: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
5.24 For three mutually exclusive events, P(A) 5 0.3, P(B) 5 0.6, and P(A or B or C) 5 1.0. What is the value of P(A or C)?
5.23 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?Source: McDonald’s
5.22 A survey of employees at a large company found the following relative frequencies for the one-way distances they 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
5.21 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
5.20 Determine the number of combinations and the number of possible permutations of n objects r at a time.
5.20 Use Bayes’ theorem and additional information to revise a probability.
5.20 Construct and interpret a tree diagram with sequential events.
5.20 Determine the probability that an event will occur.
5.20 Interpret a contingency table in terms of the probabilities associated with the two variables.
5.20 Understand the basic concept of probability, including the classical, relative frequency, and subjective approaches.
5.20 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
5.19 According to data from the U.S. Energy Infor ma tion Administration, the 60.0 million U.S. house holds 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
5.18 A shopping mall developer and a historical society are the only two bidders for a local historical landmark.The sealed bids are to be opened at next week’s city council meeting and the winner announced. Draw a single Venn diagram describing purchase/nonpurchase of the landmark by these two
5.17 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
5.16 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?
5.15 The following table represents gas well completions during 1986 in North and South America.a. Draw a Venn diagram that summarizes the information in the table.b. Identify the region of the Venn diagram that represents (N and D).c. Identify the region of the Venn diagram that represents (N9 and
5.14 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%?
5.13 Using the table in Exercise 5.12, how many victims were in the category described by:a. (A and A9)?b. (C or F)?c. (A9 and G9)?d. (B or G9)?
5.12 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 are identified by the letters A–C and D–G, respectively.a. For this table, identify any two events that are mutually exclusive.b. For this
5.11 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.
5.10 A sample space includes the events A, B, and C.Draw a Venn diagram in which the three events are mutually exclusive.
3.2 For each of the 20 different samples from Applet Exercise 3.1, calculate the difference between your sample proportion and the actual population proportion.(Remember to retain the positive or negative sign associated with each difference.) What was the average difference for the samples you
3.1 Take 20 different samples and for each one, record both the sample proportion and the actual population proportion.How many times was your sample proportion less than the actual population value? Equal to the actual population value? Greater than the actual population value?
4. Select a company that makes racquetball racquets, then search message boards for comments that group participants may have made about the quality or reputation of racquets carrying that company’s brand name.
3. For two of the companies that manufacture equipment for racquet sports, visit the companies’ websites and, if possible, read their most recent annual report. For each company, what have been the trends in overall company sales and profitability over the most recent years reported?
2. Who are some of the leading manufacturers of racquetball and tennis racquets? If possible, find out their relative importance in terms of manufacturing volume or retail sales of these products.
1. Approximately how much money do Americans spend on sports equipment annually? If possible, identify which types of sports equipment are the biggest sellers.
4.74 Unknown to a quality assurance technician, the tensile strengths (in pounds per square inch, psi) for all 500 heavy-duty construction bolts in a recent shipment are as listed in fi le XR04074. Because a bolt must be broken to measure its strength, the testing process is destructive. The
4.73 In 2006, the average U.S. production employee worked 38.9 hours per week. An assistant in the human resources department of Acme Eyebolts, Inc., is curious as to how the workers in her company compared to this fi gure during the fi rst week of this month. The assistant will be reaching her
4.71 Of a company’s 1000 employees, 200 are managers, 700 are factory employees, and 100 are clerical. In selecting a sample of 100 employees, a researcher starts at the beginning of the alphabet and continues until she has collected the names of 20 managers, 70 factory employees, and 10 clerical
4.70 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.
4.69 According to the U.S. Bureau of the Census, 27%of U.S. adults are college graduates. In a stratifi ed sample of 200 U.S. adults, approximately how many persons in each of the following categories should be questioned:(a) college graduate and (b) not a college graduate?Source: Statistical
4.68 Researchers at a university with an enrollment of 12,000 take a census of the entire student population, asking, “Shoplifting is not only illegal, it raises the prices that we all have to pay. Have you ever shoplifted from the university bookstore?” Based on the preceding, discuss the
4.67 A researcher wants to fi nd out to what extent local residents participate in the recreation and entertainment activities available in their community. She selects a simple random sample of numbers from the telephone directory and proceeds to call these numbers between 6 p.m.and 9 p.m. If the
4.66 Visit google.com and search message boards for postings that pertain to Sony digital cameras. Given the kinds of discussions that take place in such settings, what benefi ts could Sony obtain by having someone within the company “lurk” (i.e., observe without participating)in one or more
4.65 One of the capabilities on the Internet is called“reverse lookup.” Enter the residential telephone number for someone you know. Evaluate the accuracy of the name and address provided, along with the validity of the map that can be generated as additional information.Was the reverse lookup
4.64 Using the U.S. Bureau of the Census (census.gov) as your starting point, use the links it provides and fi nd the most recent population total for Canada.
4.63 Visit the U.S. Bureau of the Census (census.gov), and fi nd the following descriptive statistics for Kalamazoo County, Michigan:a. Of those who are 25 or older, the percentage who are high school graduatesb. The number of persons who are 65 or olderc. The median household income
4.62 Shirley will be graduating soon and is anticipating job offers from several national-level corporations. Depending on the company she joins, she could end up living in any of four different locations in the United States.a. What are some of the ways that Shirley could utilize the Internet for
4.61 In general, what are some of the considerations in evaluating the suitability of data that have been generated by someone else? For what types of sources should secondary data be regarded with special skepticism?
4.60 When customers purchase goods at a Radio Shack store, they are typically asked for their name and phone number so their purchase information can be stored. This would be one portion of the vast internal and external data available to the company. How might a company like Radio Shack utilize
4.59 Using either the Internet or the Encyclopedia of Associations, identify a group or organization that might be able to supply information ona. the popularity of bowling.b. child abuse in the United States.c. industrial accidents.d. antique and classic cars.
4.58 A security offi cer uses a one-way mirror to watch department store shoppers and identify potential shoplifters. In addition to observing whether a person is attempting to steal merchandise, what other personal or behavioral characteristics can be observed in this setting?
4.57 Timetech, Inc., has been experimenting with different approaches to improving the performance of its fi eld sales force. In a test involving salespersons in Maine, the company found that giving sales leaders a free snowmobile caused a sales increase of 25% in that state.The experiment in Maine
4.56 The curator of a fossil museum fi nds there were 1450 visitors in May and 1890 visitors in June. At the beginning of June, he had hired Bert McGruff, a popular local athlete, to serve as a tour guide. Mr. McGruff, pointing out the increase in attendance, has demanded a raise in pay.
4.55 A mail survey of junior executives is designed to measure how much time they spend reading The Wall Street Journal each day and how they 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)
4.54 To collect information on how well it is serving its customers, a restaurant places questionnaire cards on the tables, with card deposit boxes located near the exit.a. Do you think that nonresponse error might infl uence the results of this effort? In what way(s)?b. In addition to being a
4.53 In an attempt to measure the availability of component parts for a new product line, a manufacturer mails a questionnaire to 15 of the 25 companies that supply these components. Past experience with similar surveys has shown that such companies tend to exaggerate their ability to supply
4.52 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
4.51 A labor union offi cial has considered three possible negotiating stances that the union might take during upcoming contract negotiations. Members of the rank and fi le, on the other hand, could differ in terms of the approach they would most like to see. The union offi cial is concerned with
4.50 The Sonic Travel Agency has not kept pace with the current boom in family vacation air travel between the agency’s northern city and sunny Florida. For each of the following, indicate whether the associated data are primary or secondary. If the data are secondary, further indicate whether
4.49 A study found that the average American buys 4.6 movie tickets per year, compared to an average of 3.2 in Ireland. Assuming that the data values in file XR04049 represent the number of movie ticket purchases reported by 100 American respondents. Source: spartatheater.com, June 28, 2009.a.
4.48 Given the honeymoon expenditures for the 300 couples in Exercise 3.66 (file XR03066), generate a simple random sample consisting of 30 data values.
4.47 Given the 250 household electricity expenditures in Exercise 3.65 (file XR03065), generate a simple random sample consisting of 30 data values.
4.46 The manufacturer of a fast-drying, highly effective glue is concerned about the possibility that some users might accidentally glue their fingers together, raising potential legal problems for the firm. Could purposive sampling help determine the extent to which people might use the glue
4.45 What is meant by periodicity, and how can this present a problem when taking a systematic sample?Provide an example of a systematic sampling situation where periodicity could be a factor.
4.44 Using the random number table in Appendix A, select a simple random sample of 5 from the 50 states of the United States.
4.43 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
4.42 What is the difference between a probability sample and a nonprobability sample? Which type is necessary if we wish to statistically generalize from the sample to the population?
4.41 In what way are the quota sample and the stratified sample similar? In what way are they different? What effect does this difference have on the applications for which such samples might be appropriate?
4.40 Differentiate between a judgment sample and a convenience sample.
4.39 To obtain a sample of the invoices over the past year, a clerk uses the computer to select all invoice numbers that are a multiple of 13. If the invoice numbers are sequential, beginning with 1, what type of sample does this represent?
4.38 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
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