At Dolly Foods, customers spend an average of 25 minutes selecting their groceries and checking out by entering a single-line queue served by two cashiers. The service times required for the cashiers to check out customers follow an exponential distribution and average 4 minutes. Customers arrive at the cashier counter according to a Poisson distribution at the average rate of 8 customers per hour. a. Determine:
(i) the average time a customer spends in the store;
(ii) the average number of customers waiting in line prior to being checked out;
(iii) the proportion of customers who will have to wait in line.
b. What assumptions did you make in part (a)?
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