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 $3\mathrm{.}0$ per minute. In serving themselves, customers take about $17$ seconds, exponentially distributed.

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a$.$ How many customers would you expect to see, on average, at the coffee urn? $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

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b$.$ How long would you expect it to take to get a cup of coffee? $($Round your answer to $2$ decimal places.$)$

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c$.$ What percentage of time is the urn being used? $($Do not round intermediate calculations. Round your answer to $1$ decimal place.$)$

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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.$)$

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e$.$ If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constant time of $17$ 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.$)$

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f$.$ If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constant time of $17$ 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.$)$

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