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Unformatted text preview: 74 CHAPTER 4. DISCRETE RANDOM VARIABLES Exercise 4.22 The chance of a IRS audit for a tax return with over $25,000 in income is about 2% per year. We are interested in the expected number of audits a person with that income has in a 20 year period. Assume each year is independent. d. How many audits are expected in a 20 year period? e. Find the probability that a person is not audited at all. f. Find the probability that a person is audited more than twice. Exercise 4.23 (Solution on p. 83.) Refer to the previous problem. Suppose that 100 people with tax returns over $25,000 are ran- domly picked. We are interested in the number of people audited in 1 year. One way to solve this problem is by using the Binomial Distribution. Since n is large and p is small, another discrete distribution could be used to solve the following problems. Solve the following questions (d-f) using that distribution. d. How many are expected to be audited? e. Find the probability that no one was audited. f. Find the probability that more than 2 were audited. Exercise 4.24 Suppose that a technology task force is being formed to study technology awareness among in- structors. Assume that 10 people will be randomly chosen to be on the committee from a group of 28 volunteers, 20 who are technically proficient and 8 who are not. We are interested in the number on the committee who are not technically proficient. d. How many instructors do you expect on the committee who are not technically proficient? e. Find the probability that at least 5 on the committee are not technically proficient. f. Find the probability that at most 3 on the committee are not technically proficient. Exercise 4.25 (Solution on p. 83.) Refer back to Exercise 4.15.12. Solve this problem again, using a different, though still acceptable, distribution....
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- Fall '08