Hey everybody I posted this question before butI never got an answers can somebo

Question

Hey everybody I posted this question before butI never got an answers can somebody please show me how and theresult for this problem:
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 probability that for oneparticular day, there are at least two returns with errors.
b) If the agent works on a weekend and audits 30 returns, find theprobability that there will be exactly 4 returns witherrors.

Thank You, Please show all work and the ANSWERS.Will give a Lifesaver. Thanks

Explanation / Answer

a) This is a binomial distribution with n = 15 and p = .2 Asa result, the pdf is... P(X = x) = C(n, x) * p^x * (1-p)^(n-x) = C(15, x) * .2^x * .8^(15 - x) where C(n, x) = n! / (x! * (n-x)!) At least two errors = P(3) + P(4) + ... P(15) = 1 - P(0) - P(1) -P(2) P(0) = 0.03518437209 P(1) = 0.1319413953 P(2) = 0.2308974418 1 - P(0) - P(1) - P(2) = 0.6019767908 2) Using the same formula as earlier, let n = 30 instead of15. Thus, we have P(X = x) = C(30, x) * .2^x * .8^(30-x) P(X = 4) = 0.1325224483

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