Discuss the following in detail:
Q: Tom Smith's Jiffy Lube is able to serve customers in an average time of 12 minutes (negative exponential distribution). Customers arrive at the shop at an average of 3 per hour (Poisson distribution). The queue discipline is first-in, first-out and the calling population can be considered infinite.
a. What is the average number of vehicles in the system?
b. What is the average time a vehicle waits in the queue?
c. What is the probability that the shop is idle?
The Jiffy Lube now only has room for 5 vehicles to wait for service.
d. What is the probability that the parking area is full when a customer arrives?
e. What is the probability that exactly 6 cars arrive in any given hour?