Response to the following problem:
Harry's Variety Store has two checkstand locations-one at the front entrance to the store, the other at the rear. The checkstand locations are so far apart it is reasonable to expect that customers will not jockey between them. The checkstand in the front has two cashiers, while the checkstand in the rear has four. The service times for each cashier follow an exponential distribution, with a mean time of 2.5 minutes. Customers arrive at the checkstand locations according to a Poisson process.
Because there is more parking at the rear of the store, the arrival rate of customers at that checkstand averages 66 customers per hour, while the arrival rate at the front entrance checkstand averages 20 customers per hour.
a. What is the average time a customer spends waiting in line prior to beginning service at each of the two checkstand locations?
b. What is the average number of customers both waiting in line and being served at each of the two checkstand locations?
c. What is the probability that there are exactly 2 people waiting in line at the rear entrance checkstand?
d. What is the probability that there are 3 or fewer people waiting in line at the front entrance checkstand?
e. As a customer, would you prefer to check out at the front or the rear of the store? Justify your answer.