From historical data, James Larson's Car Wash in Jackson estimates that dirty cars arrive at the rate of $10$ per hour all day Saturday. With a crew workin 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. Assume Poisson arrivals an

a$)$ The average number of cars in line is cars $($round your response to three decimal places$).$

b$)$ The average time a car waits before it is washed is hours $($round your response to three decimal places$).$

c$)$ The average time a car spends in the service system is hours $($round your response to one decimal place$).$

d$)$ The utilization rate of the car wash is $($round your response to three decimal places$).$

e$)$ The probability that no cars are in the system is $($round your response to three decimal places$).$