# Exam P Practice Problem 73 – Wait Time at a Busy Restaurant

Both Problem 73-A and Problem 73-B use the following information.

A certain restaurant is very busy in the evening time during the weekend. When customers arrive, they typically have to wait for a table.

When a customer has to wait for a table, the wait time (in minutes) follows a distribution with the following density function.

$\displaystyle f(x)=\frac{1}{1800} \ x, \ \ \ \ \ \ \ \ \ 0

A customer plans to dine at this restaurant on five Saturday evenings during the next 3 months. Assume that the customer will have to wait for a table on each of these evenings.

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Problem 73-A

What is the probability that the minimum wait time for a table during the next 3 months for this customer will be more than half an hour?

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$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.24$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.25$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.36$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.42$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.75$

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Problem 73-B

What is the mean of the maximum wait time (in minutes) for a table during the next 3 months for this customer?

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$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 40.0$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 50.5$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 51.4$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 54.5$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 55.4$

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$\copyright \ 2013 \ \ \text{Dan Ma}$