Hi all i am having trouble with thisproblem: An IRS agent randomly selects 15 in

Question

Hi all i am having trouble with thisproblem:

An IRS agent randomly selects 15 income tax returns for audit. (Sheaudits 15 returns each day.) In the past, the agent has found that20% of her audited returns contain errors.

a) Find the mean number of returns with errorsper day.
b) Find the standard deviation for the number of returns witherrors per day
c) Find the probability that for one particular day, there areexactly two returns with errors.

Thank You, Please show all work, Will give aLifesaver. Thanks

Explanation / Answer

This is a binomial distribution as there are two possible outcomes:error ("success") or no error ("failure"). n = number of samples = 15 p = probability of "success" = .2 a) mean of binomial distribution = n*p = .2 * 15 = 3 b) standard deviation = sqrt(n*p*(1-p)) = sqrt(15*.2*(1-.2)) =sqrt(2.4) = 1.549 c) P(X = x) = C(n, x) * p^x * (1-p)^(n-x) = C(15, 2) * .2^2 * .8^13= [15! / (2! * (15-2)!)] * .2^2 * .8^13 = .231

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