For certain personal tax returns the IRS will compute the am

For certain personal tax returns, the IRS will compute the amount to refund a taxpayer. Suppose the Harrisburg office of the IRS processes an average of 4 returns per hour that require a refund calculation. a. What probability distribution applies to this situation? b. What is the probability the IRS processes exactly four returns in a particular hour that require 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?

Solution

For certain personal tax returns, the IRS will compute the amount to refund a taxpayer. Suppose the Harrisburg office of the IRS processes an average of 4 returns per hour that require a refund calculation. a. What probability distribution applies to this situation?

Poisson distribution is used.

b. What is the probability the IRS processes exactly four returns in a particular hour that require a refund calculation?

=4

P( x=4) = 0.1954

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

P( x=0) = 0.0183

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

P( x1) = 1-( P(x=0) = 0.9817