Problem 10-10

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 4.0 per minute. In serving themselves, customers take about 12 seconds, exponentially distributed.

e. If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constant time of 12 seconds, how many customers would you expect to see at the coffee urn (waiting and/or pouring coffee)? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

f. If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constant time of 12 seconds, how long would you expect it to take (in minutes) to get a cup of coffee, including waiting time? (Do not round intermediate calculations. Round your answer to 2 decimal places.)