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Chapter 6: Q.72 (page 403)
Explain whether the given random variable has a binomial distribution.
Lefties Exactly of the students in a school are left-handed.
The given distributon is binomial
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52. Study habits The academic motivation and study habits of female students as a group are better than those of males. The Survey of Study Habits and Attitudes is a psychological test that measures these factors. The distribution of scores among the women at a college has meanand standard deviation , and the distribution of scores among male students has mean and standard deviation You select a single male student and a single female student at random and give them the test.
(a) Explain why it is reasonable to assume that the scores of the two students are independent.
(b) What are the expected value and standard deviation of the difference (female minus male) between their scores?
(c) From the information given, can you find the probability that the woman chosen scores higher than the man? If so, find this probability. If not,
explain why you cannot.
14. . Life insurance A life insurance company sells a term insurance policy to a -year-old male that pays if the insured dies within the next years. The probability that a randomly chosen male will die each year can be found in mortality tables. The company collects a premium of each year a payment for the insurance. The amount that the company earns on this policy is per year, less the that it must pay if the insured dies. Here is a partially completed table that shows information about risk of mortality and the values of profit earned by the company:
(a) Copy the table onto your paper. Fill in the missing values of .
(b) Find the missing probability. Show your work.
(c) Calculate the mean .Interpret this value in context
A small ferry runs every half hour from one side of a large river to the other. The number of cars on a randomly chosen ferry trip has the probability distribution shown below. You can check that and .
(a) The cost for the ferry trip is . Make a graph of the probability distribution for the random variable money collected on a randomly selected ferry trip. Describe its shape.
(b) Find and interpret .
(c) Compute and interpret .
88. Scrabble In the game of Scrabble, each player begins by drawing 7 tiles from a bag containing tiles. There are vowels, consonants, and blank tiles in the bag. Cait chooses her tiles and is surprised to discover that all of them are vowels. Can we use a binomial distribution to approximate this probability? Justify your answer
Benford’s 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’s law (Exercise 5). What’s the expected value of the first digit? Explain how this information could be used to detect a fake expense report.
(c) What’s ? According to Benford’s law, what proportion of first digits in the employee’s expense amounts should be greater than ? How could this information be used to detect a fake expense report?
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