In a certain garage, there are three mechanics per work shift of eight hours. The garage is open 24 hours a day. Customers arrive according to a Poisson process with rate λ = 2.5 per hour. The time a mechanic takes to perform an arbitrary task is an exponential random variable with mean equal to 30 minutes.
(a) What proportion of time are all the mechanics busy?
(b) How much time, on average, must a customer wait for his car to be ready?