Problem 7-19

A cafeteria serving line has a coffee urn from which customersserve themselves. Arrivals at the urn follow a Poisson distributionat the rate of three per minute. In serving themselves, customerstake about 15 seconds, exponentially distributed.

a. How many customers would you expect to seeon the average at the coffee urn?

Average no of customers           

b. How long would you expect it to take to get acup of coffee?

Expected time            minute(s)

c.

What percentage of time is the urn being used?

Percentage of time            %

d. What is the probability that three or morepeople are at the coffee urn? (Do not round intermediatecalculations. Round your answer to 1 decimal place.)

Probability            %

e. If the cafeteria installs an automaticvendor that dispenses a cup of coffee at a constant time of 15seconds, how many customers would you expect to see at the coffeeurn (waiting and/or pouring coffee)? (Round your answer to2 decimal places.)

Average no of customers           

f. If the cafeteria installs an automatic vendorthat dispenses a cup of coffee at a constant time of 15 seconds,how long would you expect it to take (in minutes) to get a cup ofcoffee, including waiting time? (Round your answer to 2decimal places.)

Expected time            minute(s)