Response to the following problem:
Cars travel down Euclid Avenue at the mean rate of 12,000 per hour. The probability that a car will stop at the drive-thru window of Dinkie Donuts is .003. Hence, the arrival process of cars can be modeled using the Poisson distribution with average arrival rate λ = 36 per hour. The average time it takes to serve a customer is 75 seconds. If service times follow an exponential distribution, determine:
a. The average number of cars in the drive-thru line (including cars receiving service).
b. The average number of minutes a car must wait in line before being served.
c. The probability that an arriving car can be served immediately.
d. The probability that there are two or fewer cars waiting in line to be served.