A university cafeteria line in the student center is a self service 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 four per minute according to a Poisson distribution. The single cashier ringing up sales takes 12 seconds per customer on average, following an exponential distribution.

a. What is the probability that there are more than two students in the system?

(b) What is the probability that the system is empty?

(c) On average how long will a student have to wait before reaching the cashier?

(d) What is the average number of students in the queue for the cashier?

(e) What is the average number of students in the system?