Automobiles arrive at the drive-through window at the downtown Urbana, Illinois, post office at the rate of

Question:

Automobiles arrive at the drive-through window at the downtown Urbana, Illinois, post office at the rate of 4 every 10 minutes. The average service time is 2 minutes. The Poisson is appropriate for the arrival rate and service times are exponentially distributed.
(a) What is the average time a car is in the system?
(b) What is the average number of cars in the system?
(c) What is the average number of cars waiting to receive service?
(d) What is the average time a car is in the queue?
(e) What is the probability that there are no cars at the window?
(f) What percentage of the time is the postal clerk busy?
(g) What is the probability that there are exactly 2 cars in the system?
(h) By how much would your answer to part (a) be reduced if a second drive-through window, with its own server, were added?

Distribution
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