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 working the wash$$ line, James 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. Assume Poisson arrivals and negative exponential service times.

Part $2$

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

Part $3$

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

Part $4$

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

Part $5$

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

Part $6$

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