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 10 seconds, exponentially distributed.

d. What is the probability that three or more people are in the cafeteria? (Round your intermediate calculations to 3 decimal places and final answer to 1 decimal place.)

e. If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constant time of 10 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 10 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.)