Q. A cafeteria serving line has a coffee urn from which customers serve themselves. Arrivals at the urn follow a Poisson distribution at the rate of 3 per minute. In serving themselves, customers take about 15 seconds, exponentially distributed.

a) Explain how many customers would you expect to see on the average at the coffee urn?

b) Explain how long would you expect it to take to get a cup of coffee?

c) Illustrate what is the probability that 3 or more people are in the cafeteria?

d) If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constant time of 15 seconds, explain how does this change your answers to a and b?