A crew of mechanics at the Highway Department Garage repair vehicles that break down at an average of $=7\mathrm{.}5$ vehicles per day $($approximately Poisson in nature$).$ The mechanic crew can service an average of $=10$ vehicles per day with a repair time distribution that approximates an exponential distribution.

a$.$ What is the utilization rate for this service system?

b$.$ What is the average time before the facility can return a breakdown to service?

c$.$ How much of that time is spent waiting for service?

d$.$ How many vehicles are likely to be in the system at any one time?