A student majoring in Accounting is trying to decide upon th

A student majoring in Accounting is trying to decide upon the number of firms to which she should apply. Given her work experiences, grades, and extracurricular activities, a placement counselor estimates that she can expect to receive job offers from 80% of the firms to which she applies. Wanting to save time, the student applies to only five firms. Assuming that the counselor

Solution

Given X follows Binomial distribution with n=5 and p=0.8

P(X=x)=5Cx*(0.8^x)*(0.2^(5-x)) for x=0,1,2,3,4,5

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a. No offers

P(X=0) =5C0*(0.8^0)*(0.2^(5-0)) =0.00032

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b. At most two offers

P(X<=2) =P(X=0)+P(X=1)+P(X=2) =0.05792

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c. Between two and four offers

P(2<=X<=4) = P(X=2)+P(X=3)+P(X=4) =0.6656
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d. Five offers

P(X=5) =0.32768

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e. Fewer than four offers

P(X<4) = P(X=0)+P(X=1)+P(X=2)+P(X=3) =0.26272
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f. At least one offers

P(X>=1) =1-P(X=0) =0.99968