Question: A cafeteria serving line has coffee urn from which customers serve themselves. Arrivals at the urn follow a Poisson distribution at the rate of 2.5

A cafeteria serving line has coffee urn from which customers serve themselves. Arrivals at the urn follow a Poisson distribution at the rate of 2.5 per minute. In serving themselvescustomers take about 15 secondsexponentially distributed.

a. How many customers would you expect to see, on average, at the coffee urn?

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

c. What percentage of the time is the urn being used?

d. What is the probability that three or more people are in the cafeteria?

e. the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constant time of 15 seconds, how many customers would you expect to see at the coffee urn (waiting and/or pouring coffee)?

f. If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constant time of 15 secondshow long would you expect it to take (in minutes) to get a cup of coffeeincluding waiting time ?

Please show calculations for each question.

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