On average, 4 customers per hour use the public telephone in the sheriff’s detention 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 minutes. The sheriff will install a second telephone booth when an arrival can expect to wait 3 minutes or longer for the phone.

a) By how much must the arrival rate per hour increase to justify a second telephone booth?

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

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