Customers arrive at Paul Harrold’s Styling Shop at a rate of 3 per hour, distributed in a Poisson fashion. Paul can perform haircuts at a rate of 5 per hour, distributed exponentially.
(a) Find the average number of customers waiting for haircuts.
(b) Find the average number of customers in the shop.
(c) Find the average time a customer waits until it is his or her turn.
(d) Find the average time a customer spends in the shop.
(e) Find the percentage of time that Paul is busy.