Two hundred thirty employee travel expense reimbursement vouchers were filed las

Question

Two hundred thirty employee travel expense reimbursement vouchers were filed last year in the finance department at Ramjac Corporation. Of these, 22 contained errors. A corporate auditor audits a sample of seven vouchers. Let X be the number of incorrect vouchers in the sample. (a) Is the binomial approximation justified? O Yes O No (b) Find the probability that the sample contains no erroneous vouchers. (Do not round your intermediate answers. Round your answer to 4 decimal places.) Probability (c) 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.) Probability

Explanation / Answer

Solution:-

a) Yes, the binomial approximation is justified.

b) The probability that the sample contains no erroneous vouchers is 0.4423.

p = 22/200 = 0.11, n = 7

x = 0

By applying binomial distribution:-

P(x,n) = nCx*px*(1-p)(n-x)

P(x = 0) = 0.4423

c) The probability that the sample contains atleast two erroneous vouchers is 0.1750.

p = 22/200 = 0.11, n = 7

x = 2

By applying binomial distribution

P(x,n) = nCx*px*(1-p)(n-x)

P(x > 2) = 0.1750

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