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business
business statistics a first course

Questions and Answers of Business Statistics A First Course

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
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
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
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
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.
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
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.
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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,
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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,
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
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?
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
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
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.
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
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

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