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Chapter 6: Q. 1.2 (page 385)
For each of the following situations, determine whether the given random variable has a binomial distribution. Justify your answer.
Choose three students at random from your class. Let the number who are over feet tall.
No, the variable is not binomial distribution.
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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?
A large auto dealership keeps track of sales made during each hour of the day. Let = the number of cars sold during the 铿乺st hour of business on a randomly selected Friday. Based on previous records, the probability distribution of is as follows:
The random variable has mean and standard deviation .
To encourage customers to buy cars on Friday mornings, the manager spends to provide coffee and doughnuts. The manager鈥檚 net pro铿乼 on a randomly selected Friday is the bonus earned minus this . Find the mean and standard deviation of.
90. Normal approximation To use a Normal distribution to approximate binomial probabilities, why do we require that both and be at least ?
51. His and her earnings A study of working couples measures the income of the husband and the income of the wife in a large number of couples in which both partners are employed. Suppose that you knew the means and and the variances and of both variables in the population.
(a) Is it reasonable to take the mean of the total income to be ? Explain your answer.
(b) Is it reasonable to take the variance of the total income to be ? Explain your answer.
Statistics for investing (3.2) Joe's retirement plan invests in stocks through an "index fund" that follows the behavior of the stock market as a whole, as measured by the Standard & Poor's (S&P) 500 stock index. Joe wants to buy a mutual fund that does not track the index closely. He reads that monthly returns from Fidelity Technology Fund have correlation with the index and that Fidelity Real Estate Fund has correlation role="math" localid="1649424494964" with the index.
(a) Which of these funds has the closer relationship to returns from the stock market as a whole? How do you know?
(b) Does the information given tell Joe anything about which fund has had higher returns?
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