Question

The Internal Revenue Service is studying the category of charitable contributions. A sample of 22 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 22 returns, 7 had charitable contributions of more than $1,000. Suppose 6 of these returns are selected for a comprehensive audit.

1. Explain why the hypergeometric distribution is appropriate. Because: (Pick one)

• you are sampling a small population without replacement.

• you are sampling a small population with replacement.

• you are sampling a large population without replacement.

B. What is the probability exactly one of the six audited had a charitable deduction of more than $1,000? (Round your answer to 4 decimal places.)

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.)

Answer 1

a) you are sampling a small population without replacement.

b) P(X=1)= C(7,1)*C (15,5)/C(22,6)           =   0.2817

c) P(x≥1) = 1 - P(X=0) = 1 - C(7,0)*C (15,6)/C(22,6)           = 1 - 0.0671 =0.9329