Two hundred and eighty employee travel expense reimbursement

Two hundred and eighty employee travel expense reimbursement vouchers were filed last year in the finance department at Ramjac Corporation. Of these, 27 contained errors. A corporate auditor audits a sample of twelve vouchers. Let X be the number of incorrect vouchers in the sample.

Find the probability that the sample contains no erroneous vouchers. (Do not round your intermediate answers. Round your answer to 4 decimal places.)

Find the probability that the sample contains at least two erroneous vouchers. (Do not round your intermediate answers. Round your answer to 4 decimal places.)

Solution

(a)Yes.

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(b) Given X follows Binomial distribution with n=12, p=27/280 =0.09642857

P(X=x)=12Cx*(0.09642857^x)*(1-0.09642857)^(12-x)

So the probabilty is

P(X=0) =12C0*(0.09642857^0)*(1-0.09642857)^(12-0) =0.2962

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(c) P(X>=2)=1-P(X=0)-P(X=1) =0.3245