Question;Chap 5: 6, 14, 24, 34, 40, 52, 60, 74, 78, 82 5-6 Consider the following discrete probability distribution: x P(x) 3 0.13 6 0.12 9 0.15 12 0.6 a Calculate the variance and standard deviation of the random variable. b Let y = x + 7. Calculate the variance and standard deviation of the random variable y. c Let z = 7x. Calculate the variance and standard deviation of the random variable z. d From your calculations in part and part b, indicate the effect that adding a constant to a random variable has on its variance and standard deviation. e From your calculations in part a and part c, indicate the effect that multiplying a random variable with a constant has on the variance and the standard deviation of the random variable. 5-14 Cramer's Bar and Grille in Dallas can seat 130 people at a time. The manager has been gathering data on the number of minutes a party of four spends in the resteraunt from the moment they are seated to when they pay for the check. What is the mean number of minutes for a dinner party of four. What is the variance and standard deviation? # of Mins Probability 60 0.05 70 0.15 80 0.2 90 0.45 100 0.1 110 0.05 5-24 Use the bionomial formula to calculate the following probabilities for an experiment in which n=5 and p =.4: a the probability that x is at most 1. b the probability that x is at least 4. c the probability that x is at less than 1. 5-34 Magic Valley Memorial Hospital administrators have recently received an internal audit report that indicates that 15% of all patient bills contain an error of one form or another. After spending considerable effort to improve the hospitals billing process, the administrators are convinced that things have improved. They believe that the new error rate is somewhere closer to.05. a Suppose that recently the hospital has randomly sampled 10 patient bills and conducted a thorough study to determine whether an error exists. Assuming that managersare correct that they have improved the error rate to.05, what is the probability that they would find 3 or more errors in a sample of 10 bills. b Referring to part A, what conclusion would you reach based on the probability of find 3 or more errors in the sample of 10 bills. 5-40 Nielsen is the major media measurement company and conduct surveys to determine household viewing choices. The following table shows the top 10 broadcast television programs for the week of January 23, 2012. Rank Program Network HH Rating** Viewers*** 1 American Idol - Wed FOX 11.1 19671 2 American Idol - Thurs FOX 10 17141 3 Big Bang Theory CBS 9.7 16130 4 CSI CBS 9 14257 5 Criminal Minds CBS 8.7 13815 6 NCIS CBS 8.1 12548 7 Undercover Boss CBS 7.9 13151 8 AFC-NFC NBC 7.3 12498 9 The Good Wife CBS 7.2 11083 10 60 Minutes CBS 7.1 11188 a Suppose that the producers of NCIS commissioned a study that called for the consultants to randomly call 25 people immediately after the NCIS time slot and interview those who said that they had just watched NCIS. Suppose the consultant submits a report sayingthat it found no one in the sample of 25 homes who claimed to have watched the programand therefore did not do any surveys. What is the probability of this happening, assuming that the Nielsen ratings for the show are accurate? b Assume the producers of the Big Bang theory planned to survey 1000 people the day following the broadcast of the program. The purpose of the sruvey was to determine what the reactions would be if one of the leading characters was retired from the show. Based on the Nielsons ratings, what would be the expected number of people who would end up being included in the analysis, assuming that all 1000 people could be reached? 5-52 Consider a situation in which a used-car lot contains five Fords, four general motors (GM) cars, and give Toyotas. If five cars were selected at random to be placed on a special sales, what is the probability that three are Fords and two are GM's? 5-60 When things are operating properly, E-Bank United, an Internet Bank, can process a maximum of 25 electronic transfers every minute during the busiest periods of the day. If it receive more transfer requests than this, then the bank's computer system will become overburdened that it will show to the point that no electronic trnasfers can be handled. If during the busiest periods of the day requests for electronic trnasfers arrive at the rate of 170 per 10-minute period on average, what is the probability that the system will be overwhelmed by requests? Assume that the process can be described by using a Poisson distribution. 5-74 Discuss the basic differences of the binomial distribution and the Poisson distribution. 5-78 The Ziteck Corporation buys parts from international suppliers. One part is currently being purchased from a Malaysian supplier under a contract that calls for at most 5% of the 10,000 parts to be defective. When a shipment arrives, Ziteck randomly samples 10 parts. If it find 2 or fewer defectives in the sample, it keeps the shipment, otherwise, it returns the entire shipment to the supplier. a Assumming that the conditions for the binomial distribution are satisfied, what is the probability that the sample will lead Ziteck to keep the shipme+B118nt if the defect rate is.05? b Suppose the supplier is actually sending Ziteck 10% defects. What is the probability that the sample will lead Ziteck to accept the shipment anyways? c Comment on this sampling plan (sample size and accept/reject point). Do you think it favors either Ziteck or the supplier, Discuss. 5-82 VERCOR provides merger and acquisiton consultants to assist corporations when owners decide to offer their business for sale. One of its new releases, "Tax Audit Frequency is Rising" writted by David L. Perkins Jr.. A VERCOR partner, and which orginally appeared in the Business Owner, indicated that the proportion of the largest businesses, those corporations with asses of $10 million and over, that were audited was.17. a One member of VERCORS board of directors is on the board of directors of four other large corporations. Calculate the expected numberof these five corporations that should get audited, assuming selection is random. b Three of the five corporations were actually audited. Determine the probability that at least three of the five corporations would be audited if 17% of large corporations were audited. (Assume random selection). c The board member is concerned that the corporations have been singled out to be audited by the Internal Revenue Service. Respond to these throughts using probability and statistic logic.
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