The Internal Revenue Service is studying the category of charitable contribution

Question

The Internal Revenue Service is studying the category of charitable contributions. A sample of 20 returns is selected from young couples between the ages of 20 and 35 who had an adjusted gross income of more than $100,000. Of these 20 returns, 6 had charitable contributions of more than $1,000. Suppose 4 of these returns are selected for a comprehensive audit. a. Explain why the hypergeometric distribution is appropriate. Because you are sampling a small population without replacem ent. O you are sampling a small population with replacement. Oyou are sampling a large population without replacement. b. What is the probability exactly one of the four audited had a charitable deduction of more than $1,000? (Round your answer to 4 decimal places.) Probability C. What is the probability at least one of the audited returns had a charitable contribution of more than $1,000? (Round your answer to 4 decimal places.) Probability

Explanation / Answer

a) Option-A) you are sampling a samll population without replacement

b) N = 20

k = 6

n = 4

P(X = 1) = 6C1 * 14C3 / 20C4 = 0.4508

c) P(X > 1) = 1 - P(X = 0) = 1 - 6C0 * 14C4 / 20C4 = 1 - 0.2066 = 0.7934

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