Suppose the Internal Revenue Service is studying the category of charitable

Chapter 0, Problem 54

(choose chapter or problem)

QUESTION:

Suppose the Internal Revenue Service is studying the category of charitable contributions. A sample of 25 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 25 returns, five had charitable contributions of more than $1,000. Suppose four of these returns are selected for a comprehensive audit. a. Explain why the hypergeometric distribution is appropriate. b. What is the probability exactly one of the four audited had a charitable deduction of more than $1,000? c. What is the probability at least one of the audited returns had a charitable contribution of more than $1,000?

Questions & Answers

QUESTION:

ANSWER:

Step 1 of 3

(a) A hypergeometric distribution needs to be used when we are interested in the number of successes in a sample, when the sample comes from a population with successes and failures.

In this case, we have a set of 25 returns of which 5 had charitable contributions and thus did not have charitable contributions. When we consider a success to be a charitable contribution, then the sample thus has indeed a hypergeometric distribution as we select a sample of 4 returns.