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 26 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 26 returns, 6 had charitable contributions of more than $1,000. Suppose 5 of these returns are selected for a comprehensive audit. a You should use the hypergeometric distribution is appropriate. Because b. What is the probability exactly one of the five audited had a charitable deduction of more than $1,000? (Round your answer to 4 decimal places.) Probability 0.4419 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 You should use the hypergeometric distribution is appropriate. Because

the distributuon as you can see follow a hypergeomtric distribution

b)

P(x=1) = 6C1 * 20C4 / 26C5 = 0.4419

c)

P(x=0) = 6C0 * 20C5 / 26C5 = 0.2357

P( x >=1 ) = 1 - 0.4419 - 0.2357 = 0.3224

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