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 32 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 32 returns, 7 had charitable contributions of more than $1,000. Suppose 6 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 six 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

B.

Note that the probability of x successes out of n trials is          
          
P(x) = C(N-K, n-x) C(K, x) / C(N, n)          
          
where          
N = population size =    32      
K = number of successes in the population =    7      
n = sample size =    6      
x = number of successes in the sample =    1      
          
Thus,          
          
P(   1   ) =    0.410409714 [ANSWER]

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c)

Note that the probability of x successes out of n trials is          
          
P(x) = C(N-K, n-x) C(K, x) / C(N, n)          
          
where          
N = population size =    32      
K = number of successes in the population =    7      
n = sample size =    6      
x = number of successes in the sample =    0      
          
Thus,          
          
P(   0   ) =    0.195433197

Thus, P(at least 1) = 1 - P(0) = 0.804566803 [ANSWER]

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