$.$ From historical data, AVM Car Wash estimates that dirty cars arrive at the rate of

$10$ per hour all day Saturday. With a crew working the wash line, AVM 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 spends in the service system.

c$.$ utilization rate of the car wash.

d$.$ probability that no cars are in the system