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 28 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 28 returns, 5 had charitable contributions of more than $1,000. Suppose 4 of these returns are selected for a comprehensive audit. a. You should use the distribution is appropriate. Because 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) Small population is sampled here without replacement

b) A sample of 28 returns is selected. Of these 28 returns 5 had charitable contributions of more than $1,000.
P(exactly 1 charitable deduction) = (5C1)(23C3)/(28C4) = 0.4325

c) P(at least one contribution) = 1 - P(no contribution)
= 1 -  [(5C0)(23C4)/(28C4)]= 0.5675

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