Question 569959: Suppose 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)What is the probability exactly one of the six audited had a charitable deduction of more than $1,000?
(b)What is the probability at least one of the audited returns had a charitable contribution of more than $1,000?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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.
p-hat = 7/32
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Suppose 6 of these returns are selected for a comprehensive audit.
(a)What is the probability exactly one of the six audited had a charitable deduction of more than $1,000?
Binomial with n = 6 and p(had) = 7/32 ; p(not had) = 25/32
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P(x = 1) = 6C1(7/32)(25/32)^5 = binompdf(6,7/32,1) = 0.3820
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(b)What is the probability at least one of the audited returns had a charitable contribution of more than $1,000?
P(at least one) = 1 - P(none)
= 1 - (5/32)^6
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= 1 - 0.0000146
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= 0.9999
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Cheers,
Stan H.
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