cafeteria serving line has a coffee urn from which customers serve themselves. Arrivals at the urn follow a Poisson distribution at the rate of 3.0 per minute. In serving themselves, customers take about 30 seconds, exponentially distributed.

(a) How long would you expect it to take to get a cup of coffee, including waiting time?

(b) If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constant time of 22 seconds, how long would you expect it to take (in minutes) to get a cup of coffee, including waiting time?