3. For certain personal tax returns, the IRS will compute the amount to refund a

Question

3. For certain personal tax returns, the IRS will compute the amount to refund a taxpayer. Suppose the Chicago office of the IRS processes an average of three returns per hour that require a refund calculation.

a. What probability distribution applies to this situation?

b. What is the probability that the IRS processes exactly three refunds in a particular hour that requires a refund calculation?

c. What is the probability the IRS does not compute a refund on any return in an hour?

d. What is the probability the IRS processes at least one return in a particular hour that requires a refund calculation

Explanation / Answer

A) This is poisson distribution with mean 3

P(X = x) = e-3 * 3x / x!

B) P(X = 3) = e-3 * 33 / 3! = 0.2240

C) P(X = 0) =e-3 * 30 / 0! = 0.0498

D) P(X > 1) = 1 - P(X =0) = 1 - 0.0498 = 0.9502

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