1 . A cafeteria line in the Union at Towson University 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 arrival rate () and service rate()for the system?

(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 waiting in the queue to pay the cashier?

(e) The probability ofthree or more than threestudents in the system