# Exam P Practice Problem 79 – wait time at a bank

When a customer walks into a branch office of a certain large national bank for routine banking service (e.g. making cash deposits or making cash withdrawals), he or she will be served right away if one of the bank tellers is available. If all bank tellers are busy, the wait time for a bank teller (in minutes) follows a distribution with the following density function:

$\displaystyle f(t)=\frac{2}{25} \ (5-t) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0

Problem 79-A

On one particular day, the branch office is short staffed. As a result, the wait time for a bank teller is 25% longer than usual. When a customer has to wait, what is the mean wait time on this day?

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$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{5}{12} \text{ minutes}$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{20}{12} \text{ minutes}$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{25}{12} \text{ minutes}$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{40}{12} \text{ minutes}$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{50}{12} \text{ minutes}$

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Problem 79-B

On one particular day, the branch office is short staffed. As a result, the wait time for an bank teller is 25% longer than usual. When there is a need to wait on this day, what is the probability that a customer has to wait more than 3.75 minutes for a bank teller?

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$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.0625$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.0695$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.1200$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.1600$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.1950$

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$\copyright \ 2014 \ \ \text{Dan Ma}$