14.4. On average, 4 customers per hour use the public telephone in the sheriff's de- tention area, and this use has a Poisson distribution. The length of a phone call varies according to a negative exponential distribution, with a mean of 5 min- utes. The sheriff will install a second telephone booth when an arrival can ex- pect to wait 3 minutes or longer for the phone.

a. By how much must the arrival rate per hour increase to justify a second tele- phone booth?

b. Suppose the criterion for justifying a second booth is changed to the follow- ing: install a second booth when the probability of having to wait at all ex- ceeds 0.6. Under this criterion, by how much must the arrival rate per hour increase to justify a second booth?