Problem $10-10($Algo$)$

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 $2\mathrm{.}0$ per minute. In serving themselves, customers take about $20$ seconds, exponentially distributed.

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

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

Average number of customers

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

Note: Round your answer to $2$ decimal places.

Expected time

minute$($s$)$

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

Note: Do not round intermediate calculations. Round your answer to $1$ decimal place.

Percentage of time

$\%$

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

Note: Round your intermediate calculations to $3$ decimal places and final answer to $1$ decimal place.