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Chapter 6: Q. 102 (page 406)
In the previous exercise, the probability that at least of Joe's eggs contains salmonella is about
(a) .
(b) .
(c) .
(d) .
(e) .
(c) (at least salmonella)
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A large auto dealership keeps track of sales and leases agreements made during each hour of the day. Let = the number of cars sold and = the number of cars leased during the 铿乺st hour of business on a randomly selected Friday. Based on previous records, the probability distributions of and are as follows:
顿别铿乶别
The dealership鈥檚 manager receives a bonus for each car sold and a bonus for each car leased. Find the mean and standard deviation of the manager鈥檚 total bonus . Show your work.
Lie detectors A federal report finds that lie detector tests given to truthful persons have probability about of suggesting that the person is deceptive. A company asks job applicants about thefts from
previous employers, using a lie detector to assess their truthfulness. Suppose that all answer truthfully. Let the number of people who the lie detector says are being deceptive.
(a) Find and interpret .
(b) Find and interpret .
54. The Tri -State Pick Refer to Exercise . Suppose
(a) Find the mean and standard deviation of your total winnings. Show your work.
(b) Interpret each of the values from (a) in context .
The deck of cards contains hearts. Here is another wager: Draw one card at random from the deck. If the card drawn is a heart, you win . Otherwise, you lose . Compare this wager (call it Wager 2) with that of the previous exercise (call it Wager ). Which one should you prefer?
(a) Wager , because it has a higher expected value.
(b) Wager , because it has a higher expected value.
(c) Wager , because it has a higher probability of winning.
(d) Wager , because it has a higher probability of winning. (e) Both wagers are equally favorable
Benford鈥檚 law and fraud A not-so-clever employee decided to fake his monthly expense report. He believed that the first digits of his expense amounts should be equally likely to be any of the numbers from to . In that case, the first digit of a randomly selected expense amount would have the probability distribution shown in the histogram.
(a). Explain why the mean of the random variable Y is located at the solid red line in the figure.
(b) The first digits of randomly selected expense amounts actually follow Benford鈥檚 law (Exercise 5). What鈥檚 the expected value of the first digit? Explain how this information could be used to detect a fake expense report.
(c) What鈥檚 ? According to Benford鈥檚 law, what proportion of first digits in the employee鈥檚 expense amounts should be greater than ? How could this information be used to detect a fake expense report?
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