Problem $7-19$

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 three per minute. In serving themselves, customers take about $15$ seconds, exponentially distributed.

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

Average no of customers

b$.$ How long would you expect it to take to get a cup 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 more people are at the coffee urn? $($Do not round intermediate calculations. Round your answer to $1$ decimal place.$)$

Probability $\%$

e$.$ If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constant time of $15$ seconds, how many customers would vou expe