From historical data, Harry's Car Wash estimates that dirty cars arrive at the rate of 10 per hour all day Saturday. With a crew working the wash line, Harry figures that cars can be cleaned at the rate of one every 5 minutes. One car at a time is cleaned in this example of a single-channel waiting line.

Assuming Poisson arrivals and exponential service times, find the

(a) Average number of cars in line.

(b) Average time a car waits before it is washed.

(c) Average time a car spends in the service system.

(d) Utilization rate of the car wash.

(e) Probability that no cars are in the system.