Customers arrive to the checkout area of New Navy according to a Poisson process at a rate of 108 customers per hour. At the checkout area, the service time of each customer is exponentially distributed, and on average each cashier can serve 12 customers per hour. The store has hired 11 cashiers to checkout customers and the checkout area consists of a single pool of cashiers with one common line in front of them.
a. What is the probability that a customer’s service time is less than 6 minutes?
b. What is the average number of customers waiting in the queue to be checked out? This does not include the customers being checked out.
c. What is the average total number of customers in the checkout area? This includes customers waiting to be checked out and customers being checked out.
d. What is the probability that there are 11 or more customers in the checkout area?
e. Suppose now that New Navy decides to replace the single common line for its customers with 11 separate lines, one line in front of each of the 11 cashiers. What is now the average number of customers waiting to be checked out? This only includes the customers who are waiting to be checked out (not the customers being served).