Solve the following problem:
A university cafeteria line in the student center is a self-serve facility in which students select the food items they want and then form a single line to pay the cashier. Students arrive at a rate of about four per minute according to a Poisson distribution. The single cashier ringing up sales takes about 12 seconds per customer, following an exponential distribution.
a. What is the probability that there are more than two students in the system? AND More than three students? AND More than four?
b. What is the probability that the system is empty?
c. How long will the average student have to wait before reaching the cashier?
d. What is the expected number of students in the queue?
e. What is the average number in the system?
f. If a second cashier is added (who works at the same pace), how will the operating characteristics computed in parts (b), (c), (d), and (e) change? Assume that customers wait in a single line and go to the first available cashier.