Decision Science - Queuing System

3. .lucier Foods has just opened a new cafeteria in Papine square just for university students. This is a selfserve facility in which the students select the food items they want and then form a single line to pay the cashier. Students arrive at a rate of about 4 per minute according to a Poisson distribution. The single cashier ringing up sales takes about 12 second: per customer. following an exponential distribution. a. What is the probability that the system is empty? b. How long will the ax-erage student have to wait before reaching the cashier? c. What is the expected number of students in the queue? d. What is the average number in the system