Missouri$$s Stephen Allen Electronics Corporation retain a service crew to repair machine breakdown that occur on a average of $=3$ per $8$ hour workday $($approximately Poisson in nature$).$ The Crew can service an of $8$ machines per workday, with a repair time distribution that resembles the exponential distribution.

A$.$ What is the utilization rate of this service system?

B$.$ What is the average downtime for a broken machine

C$.$ How many machines are waiting to be serviced at any given time?

D$.$ What is the probability that more than one machine is in the system? The probability that more than two are broken and waiting to be repaired or being serviced? More than three? More than four