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business statistics using excel
Introductory Statistics 7th Edition Prem S Mann - Solutions
5.124 Consider the following three games. Which one would you be most likely to play? Which one would you be least likely to play? Explain your answer mathematically.Game I: You toss a fair coin once. If a head appears you receive $3, but if a tail appears you have to pay $1.Game II: You buy a
5.123 A history teacher has given her class a list of seven essay questions to study before the next test.The teacher announced that she will choose four of the seven questions to give on the test, and each student will have to answer three of those four questions.a. In how many ways can the
5.122 Suppose that a certain casino has the “money wheel” game. The money wheel is divided into 50 sections, and the wheel has an equal probability of stopping on each of the 50 sections when it is spun.Twenty-two of the sections on this wheel show a $1 bill, 14 show a $2 bill, 7 show a $5
5.121 A baker who makes fresh cheesecakes daily sells an average of five such cakes per day. How many cheesecakes should he make each day so that the probability of running out and losing one or more sales is less than .10? Assume that the number of cheesecakes sold each day follows a Poisson
5.120 A high school history teacher gives a 50-question multiple-choice examination in which each question has four choices. The scoring includes a penalty for guessing. Each correct answer is worth 1 point, and each wrong answer costs 12 point. For example, if a student answers 35 questions
5.119 Residents in an inner-city area are concerned about drug dealers entering their neighborhood.Over the past 14 nights, they have taken turns watching the street from a darkened apartment. Drug deals seem to take place randomly at various times and locations on the street and average about
5.118 York Steel Corporation produces a special bearing that must meet rigid specifications. When the production process is running properly, 10% of the bearings fail to meet the required specifications. Sometimes problems develop with the production process that cause the rejection rate to exceed
5.117 Two teams, A and B, will play a best-of-seven series, which will end as soon as one of the teams wins four games. Thus, the series may end in four, five, six, or seven games. Assume that each team has an equal chance of winning each game and that all games are independent of one another. Find
5.116 Suppose the owner of a salvage company is considering raising a sunken ship. If successful, the venture will yield a net profit of $10 million. Otherwise, the owner will lose $4 million. Let p denote the probability of success for this venture. Assume the owner is willing to take the risk to
5.115 Scott offers you the following game: You will roll two fair dice. If the sum of the two numbers obtained is 2, 3, 4, 9, 10, 11, or 12, Scott will pay you $20. However, if the sum of the two numbers is 5, 6, 7, or 8, you will pay Scott $20. Scott points out that you have seven winning numbers
5.114 A high school boys’ basketball team averages 1.2 technical fouls per game.a. Using the appropriate formula, find the probability that in a given basketball game this team will commit exactly 3 technical fouls.b. Let x denote the number of technical fouls that this team will commit during a
5.113 An average of 1.4 private airplanes arrive per hour at an airport.a. Find the probability that during a given hour no private airplane will arrive at this airport.b. Let x denote the number of private airplanes that will arrive at this airport during a given hour.Write the probability
5.112 An average of 6.3 robberies occur per day in a large city.a. Using the Poisson formula, find the probability that on a given day exactly 3 robberies will occur in this city.b. Using the appropriate probabilities table from Appendix C, find the probability that on a given day the number of
5.111 The student health center at a university treats an average of seven cases of mononucleosis per day during the week of final examinations.a. Using the appropriate formula, find the probability that on a given day during the finals week exactly four cases of mononucleosis will be treated at
5.110 Alison Bender works for an accounting firm. To make sure her work does not contain errors, her manager randomly checks on her work. Alison recently filled out 12 income tax returns for the company’s clients. Unknown to anyone, 2 of these 12 returns have minor errors. Alison’s manager
5.109 Uniroyal Electronics Company buys certain parts for its refrigerators from Bob’s Corporation. The parts are received in shipments of 400 boxes, each box containing 16 parts. The quality control department at Uniroyal Electronics first randomly selects 1 box from each shipment and then
5.108 Twenty corporations were asked whether or not they provide retirement benefits to their employees.Fourteen of the corporations said they do provide retirement benefits to their employees, and 6 said they do not. Five corporations are randomly selected from these 20. Find the probability
5.107 In a list of 15 households, 9 own homes and 6 do not own homes. Four households are randomly selected from these 15 households. Find the probability that the number of households in these 4 who own homes isa. exactly 3b. at most 1c. exactly 4
5.106 One of the toys made by Dillon Corporation is called Speaking Joe, which is sold only by mail.Consumer satisfaction is one of the top priorities of the company’s management. The company guarantees a refund or a replacement for any Speaking Joe toy if the chip that is installed inside
5.105 Maine Corporation buys motors for electric fans from another company that guarantees that at most 5% of its motors are defective and that it will replace all defective motors at no cost to Maine Corporation. The motors are received in large shipments. The quality control department at Maine
5.104 At the Bank of California, past data show that 8% of all credit card holders default at some time in their lives. On one recent day, this bank issued 12 credit cards to new customers. Find the probability that of these 12 customers, eventuallya. exactly 3 will defaultb. exactly 1 will
5.103 Spoke Weaving Corporation has eight weaving machines of the same kind and of the same age.The probability is .04 that any weaving machine will break down at any time. Find the probability that at any given timea. all eight weaving machines will be broken downb. exactly two weaving machines
5.102 GESCO Insurance Company charges a $350 premium per annum for a $100,000 life insurance policy for a 40-year-old female. The probability that a 40-year-old female will die within 1 year is .002.a. Let x be a random variable that denotes the gain of the company for next year from a$100,000 life
5.101 Based on its analysis of the future demand for its products, the financial department at Tipper Corporation has determined that there is a .17 probability that the company will lose $1.2 million during the next year, a .21 probability that it will lose $.7 million, a .37 probability that it
5.100 Let x be the number of emergency root canal surgeries performed by Dr. Sharp on a given Monday.The following table lists the probability distribution of x.x 0 1 2 3 4 5 P(x) .13 .28 .30 .17 .08 .04 Calculate the mean and standard deviation of x. Give a brief interpretation of the value of the
5.99 Let x be the number of cars that a randomly selected auto mechanic repairs on a given day. The following table lists the probability distribution of x.x 2 3 4 5 6 P(x) .05 .22 .40 .23 .10 Find the mean and standard deviation of x. Give a brief interpretation of the value of the mean.
*5.98 Twenty percent of the cars passing through a school zone are exceeding the speed limit by more than 10 mph.a. Using the Poisson formula, find the probability that in a random sample of 100 cars passing through this school zone, exactly 25 will exceed the speed limit by more than 10 mph.b.
*5.97 On average, 20 households in 50 own answering machines.a. Using the Poisson formula, find the probability that in a random sample of 50 households, exactly 25 will own answering machines.b. Using the Poisson probabilities table, find the probability that the number of households in 50 who own
5.96 An average of .8 accidents occur per day in a particular large city.a. Find the probability that no accident will occur in this city on a given day.b. Let x denote the number of accidents that will occur in this city on a given day. Write the probability distribution of x.c. Find the mean,
5.95 An insurance salesperson sells an average of 1.4 policies per day.a. Using the Poisson formula, find the probability that this salesperson will sell no insurance policy on a certain day.b. Let x denote the number of insurance policies that this salesperson will sell on a given day. Using the
5.94 Although Borok’s Electronics Company has no openings, it still receives an average of 3.2 unsolicited applications per week from people seeking jobs.a. Using the Poisson formula, find the probability that this company will receive no applications next week.b. Let x denote the number of
5.93 An average of 4.8 customers come to Columbia Savings and Loan every half hour.a. Find the probability that exactly 2 customers will come to this savings and loan during a given hour.b. Find the probability that during a given hour, the number of customers who will come to this savings and loan
5.92 The number of students who login to a randomly selected computer in a college computer lab follows a Poisson probability distribution with a mean of 19 students per day.a. Using the Poisson probability distribution formula, determine the probability that exactly 12 students will login to a
5.91 Despite all efforts by the quality control department, the fabric made at Benton Corporation always contains a few defects. A certain type of fabric made at this corporation contains an average of .5 defects per 500 yards.a. Using the Poisson formula, find the probability that a given piece of
5.90 A large proportion of small businesses in the United States fail during the first few years of operation.On average, 1.6 businesses file for bankruptcy per day in a particular large city.a. Using the Poisson formula, find the probability that exactly 3 businesses will file for bankruptcy on a
5.89 A university police department receives an average of 3.7 reports per week of lost student ID cards.a. Find the probability that at most 1 such report will be received during a given week by this police department. Use the Poisson probability distribution formula.b. Using the Poisson
5.88 On average, 12.5 rooms stay vacant per day at a large hotel in a city. Find the probability that on a given day exactly 3 rooms will be vacant. Use the Poisson formula.
5.87 On average, 5.4 shoplifting incidents occur per week at an electronics store. Find the probability that exactly 3 such incidents will occur during a given week at this store.
5.86 A commuter airline receives an average of 9.7 complaints per day from its passengers. Using the Poisson formula, find the probability that on a certain day this airline will receive exactly 6 complaints.
5.85 A household receives an average of 1.7 pieces of junk mail per day. Find the probability that this household will receive exactly 3 pieces of junk mail on a certain day. Use the Poisson probability distribution formula.
5.84 Let x be a Poisson random variable. Using the Poisson probabilities table, write the probability distribution of x for each of the following. Find the mean, variance, and standard deviation for each of these probability distributions. Draw a graph for each of these probability distributions.a.
5.83 Let x be a Poisson random variable. Using the Poisson probabilities table, write the probability distribution of x for each of the following. Find the mean, variance, and standard deviation for each of these probability distributions. Draw a graph for each of these probability distributions.a.
5.82 Using the Poisson formula, find the following probabilities.a. P(x 2) for 3b. P(x 8) for 5.5 Verify these probabilities using Table III of Appendix C.
5.81 Using the Poisson formula, find the following probabilities.a. P(x 1) for 5b. P(x 2) for 2.5 Verify these probabilities using Table III of Appendix C.
5.80 What is the parameter of the Poisson probability distribution, and what does it mean?
5.79 What are the conditions that must be satisfied to apply the Poisson probability distribution?
5.78 Bender Electronics buys keyboards for its computers from another company. The keyboards are received in shipments of 100 boxes, each box containing 20 keyboards. The quality control department at Bender Electronics first randomly selects one box from each shipment and then randomly selects 5
5.77 A really bad carton of 18 eggs contains 7 spoiled eggs. An unsuspecting chef picks 4 eggs at random for his “Mega-Omelet Surprise.” Find the probability that the number of unspoiled eggs among the 4 selected isa. exactly 4b. 2 or fewerc. more than 1
5.76 Six jurors are to be selected from a pool of 20 potential candidates to hear a civil case involving a lawsuit between two families. Unknown to the judge or any of the attorneys, 4 of the 20 prospective jurors are potentially prejudiced by being acquainted with one or more of the litigants.
5.75 An Internal Revenue Service inspector is to select 3 corporations from a list of 15 for tax audit purposes. Of the 15 corporations, 6 earned profits and 9 incurred losses during the year for which the tax returns are to be audited. If the IRS inspector decides to select 3 corporations
5.74 Let N 16, r 10, and n 5. Using the hypergeometric probability distribution formula, finda. P(x 5)b. P(x 0)c. P(x 1)
5.73 Let N 11, r 4, and n 4. Using the hypergeometric probability distribution formula, finda. P(x 2)b. P(x 4)c. P(x 1)
5.72 Let N 14, r 6, and n 5. Using the hypergeometric probability distribution formula, finda. P(x 4)b. P(x 5)c. P(x 1)
5.71 Let N 8, r 3, and n 4. Using the hypergeometric probability distribution formula, finda. P(x 2)b. P(x 0)c. P(x 1)
5.70 Explain the hypergeometric probability distribution. Under what conditions is this probability distribution applied to find the probability of a discrete random variable x? Give one example of the application of the hypergeometric probability distribution.
5.69 A fast food chain store conducted a taste survey before marketing a new hamburger. The results of the survey showed that 70% of the people who tried this hamburger liked it. Encouraged by this result, the company decided to market the new hamburger. Assume that 70% of all people like this
5.68 Johnson Electronics makes calculators. Consumer satisfaction is one of the top priorities of the company’s management. The company guarantees a refund or a replacement for any calculator that malfunctions within 2 years from the date of purchase. It is known from past data that despite all
5.67 An office supply company conducted a survey before marketing a new paper shredder designed for home use. In the survey, 80% of the people who used the shredder were satisfied with it. Because of this high acceptance rate, the company decided to market the new shredder. Assume that 80% of all
5.66 According to a 2008 Pew Research Center survey of adult men and women, close to 70% of these adults said that men and women possess equal traits for being leaders. Suppose 70% of the current population of adults holds this view.a. Using the binomial formula, find the probability that in a
5.65 A professional basketball player makes 85% of the free throws he tries. Assuming this percentage will hold true for future attempts, find the probability that in the next eight tries, the number of free throws he will make isa. exactly 8b. exactly 5
5.64 According to Case Study 4–2 in Chapter 4, the probability that a baseball player will have no hits in 10 trips to the plate is .0563, given that this player has a batting average of .250. Using the binomial formula, show that this probability is indeed .0563.
5.63 According to an October 27, 2006 article in Newsweek, 65% of Americans said that they take expired medicines. Suppose that this result is true of the current population of Americans. Find the probability that the number of Americans in a random sample of 22 who take expired medicines isa.
5.62 Magnetic resonance imaging (MRI) is a process that produces internal body images using a strong magnetic field. Some patients become claustrophobic and require sedation because they are required to lie within a small, enclosed space during the MRI test. Suppose that 20% of all patients
5.61 According to a March 25, 2007 Pittsburgh Post-Gazette article, 30% to 40% of U.S. taxpayers cheat on their returns. Suppose that 30% of all current U.S. taxpayers cheat on their returns. Use the binomial probabilities table (Table I of Appendix C) or technology to find the probability that the
5.60 In a 2009 poll of adults 18 years and older, (BBMG Conscious Consumer Report) about half of them said that despite tough economic times, they are willing to pay more for products that have social and environmental benefits. Suppose that 50% of all such adults currently hold this view. Suppose
5.59 According to a National Public Radio poll, 46% of American school principals believe that students pay little or no attention to sex education provided in schools (http://www.npr.org/programs/morning/features/2004/jan/kaiserpoll/principalsfinal.pdf). Suppose that this result is true for the
5.58 According to a Harris Interactive poll, 52% of American college graduates have Facebook accounts(http://www.harrisinteractive.com/harris_poll/pubs/Harris_Poll_2009_04_16.pdf). Suppose that this result is true for the current population of American college graduates.a. Let x be a binomial
5.57 The binomial probability distribution is symmetric for p .50, skewed to the right for p .50, and skewed to the left for p .50. Illustrate each of these three cases by writing a probability distribution table and drawing a graph. Choose any values of n and p and use the table of binomial
5.56 Let x be a discrete random variable that possesses a binomial distribution.a. Using Table I of Appendix C, write the probability distribution of x for n 5 and p .80 and graph it.b. What are the mean and standard deviation of the probability distribution developed in part a?
5.55 Let x be a discrete random variable that possesses a binomial distribution.a. Using Table I of Appendix C, write the probability distribution of x for n 7 and p .30 and graph it.b. What are the mean and standard deviation of the probability distribution developed in part a?
5.54 Let x be a discrete random variable that possesses a binomial distribution. Using the binomial formula, find the following probabilities.a. P(x 0) for n 5 and p .05b. P(x 4) for n 7 and p .90c. P(x 7) for n 10 and p .60 Verify your answers by using Table I of Appendix C.
5.53 Let x be a discrete random variable that possesses a binomial distribution. Using the binomial formula, find the following probabilities.a. P(x 5) for n 8 and p .70b. P(x 3) for n 4 and p .40c. P(x 2) for n 6 and p .30 Verify your answers by using Table I of Appendix C.
5.52 Which of the following are binomial experiments? Explain why.a. Drawing 3 balls with replacement from a box that contains 10 balls, 6 of which are red and 4 are blue, and observing the colors of the drawn ballsb. Drawing 3 balls without replacement from a box that contains 10 balls, 6 of which
5.51 Which of the following are binomial experiments? Explain why.a. Rolling a die many times and observing the number of spotsb. Rolling a die many times and observing whether the number obtained is even or oddc. Selecting a few voters from a very large population of voters and observing whether
5.50 What are the parameters of the binomial probability distribution, and what do they mean?
5.49 Briefly explain the following.a. A binomial experimentb. A trialc. A binomial random variable
5.48 In how many ways can a sample (without replacement) of 5 items be selected from a population of 15 items?'
5.47 In how many ways can a sample (without replacement) of 9 items be selected from a population of 20 items?
5.46 A company employs a total of 16 workers. The management has asked these employees to select 2 workers who will negotiate a new contract with management. The employees have decided to select the 2 workers randomly. How many total selections are possible? Considering that the order of selection
5.45 An investor will randomly select 6 stocks from 20 for an investment. How many total combinations are possible? If the order in which stocks are selected is important, how many permutations will there be?
5.44 An environmental agency will randomly select 4 houses from a block containing 25 houses for a radon check. How many total selections are possible? How many permutations are possible?
5.43 A veterinarian assigned to a racetrack has received a tip that one or more of the 12 horses in the third race have been doped. She has time to test only 3 horses. How many ways are there to randomly select 3 horses from these 12 horses? How many permutations are possible?
5.42 An ice cream shop offers 25 flavors of ice cream. How many ways are there to select 2 different flavors from these 25 flavors? How many permutations are possible?
5.41 A ski patrol unit has nine members available for duty, and two of them are to be sent to rescue an injured skier. In how many ways can two of these nine members be selected? Now suppose the order of selection is important. How many arrangements are possible in this case?
5.40 Find the value of each of the following using the appropriate formula.6! 11! (7 2)! (15 5)! 8C2 5C0 5C5 6C4 11C7 9P6 12P8
5.39 Determine the value of each of the following using the appropriate formula.3! (9 3)! 9! (14 12)! 5C3 7C4 9C3 4C0 3C3 6P2 8P4
*5.38 Refer to the probability distribution you developed in Exercise 5.21 for the number of athletes in a random sample of two who have used illegal performance-enhancing drugs. Calculate the mean and standard deviation of x for that distribution.
*5.37 Refer to the probability distribution you developed in Exercise 5.20 for the number of lefthanded persons in a sample of two persons. Calculate the mean and standard deviation of x for that distribution.
5.36 An instant lottery ticket costs $2. Out of a total of 10,000 tickets printed for this lottery, 1000 tickets contain a prize of $5 each, 100 tickets have a prize of $10 each, 5 tickets have a prize of$1000 each, and 1 ticket has a prize of $5000. Let x be the random variable that denotes the
5.35 A contractor has submitted bids on three state jobs: an office building, a theater, and a parking garage. State rules do not allow a contractor to be offered more than one of these jobs. If this contractor is awarded any of these jobs, the profits earned from these contracts are $10 million
5.34 Refer to the probability distribution developed in Exercise 5.17 for the number of runners in a sample of two who would finish a 10K race in 49:42 or less. Compute the mean and standard deviation of x for that probability distribution.
5.33 Refer to the probability distribution you developed in Exercise 5.16 for the number of lemons in two selected cars. Calculate the mean and standard deviation of x for that probability distribution.
5.32 Refer to Exercise 5.15. Find the mean and standard deviation of the probability distribution you developed for the number of remote starting systems installed per day by Al’s Auto Security Shop over the past 80 days. Give a brief interpretation of the values of the mean and standard
5.31 Refer to Exercise 5.14. Calculate the mean and standard deviation for the probability distribution you developed for the number of defective tires on all 1300 H2 Hummer limousines. Give a brief interpretation of the values of the mean and standard deviation.
5.30 Let x be the number of potential weapons detected by a metal detector at an airport on a given day.The following table lists the probability distribution of x.x 0 1 2 3 4 5 P(x) .14 .28 .22 .18 .12 .06 Calculate the mean and standard deviation for this probability distribution and give a brief
5.29 Let x be the number of heads obtained in two tosses of a coin. The following table lists the probability distribution of x.x 0 1 2 P(x) .25 .50 .25 Calculate the mean and standard deviation of x. Give a brief interpretation of the value of the mean.
5.28 The following table, reproduced from Exercise 5.12, lists the probability distribution of the number of patients entering the emergency room during a 1-hour period at Millard Fellmore Memorial Hospital.Patients per hour 0 1 2 3 4 5 6 Probability .2725 .3543 .2303 .0998 .0324 .0084 .0023
5.27 The following table gives the probability distribution of the number of camcorders sold on a given day at an electronics store.Camcorders sold 0 1 2 3 4 5 6 Probability .05 .12 .19 .30 .20 .10 .04 Calculate the mean and standard deviation for this probability distribution. Give a brief
5.26 Let x be the number of magazines a person reads every week. Based on a sample survey of adults, the following probability distribution table was prepared.x 0 1 2 3 4 5.36 .24 .18 .10 .07 .05 Find the mean and standard deviation of x.
5.25 Let x be the number of errors that appear on a randomly selected page of a book. The following table lists the probability distribution of x.x 0 1 2 3 4 P(x) .73 .16 .06 .04 .01 Find the mean and standard deviation of x.
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