# Exam P Practice Problem 63 – Total Minutes of Telephone Calls

Problem 63-A

For a certain individual, the daily number of telephone calls (incoming or outgoing) has a Poisson distribution with mean 12. The length in time (in minutes) of each telephone call has an exponential distribution with mean 5 minutes.

The length of time of one telephone call is independent of the length of time of any other telephone call.

On a given day, this individual makes or receives 4 telephone calls. What is the probability that this person is on the telephone for more than half an hour?

$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.1218$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.1260$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.1456$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.1490$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.1512$

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Problem 63-B

For a certain individual, the daily number of telephone calls (incoming or outgoing) has a Poisson distribution with mean 16. The length in time (in minutes) of each telephone call has an exponential distribution with mean 8 minutes.

The length of time of one telephone call is independent of the length of time of any other telephone call.

On a given day, this individual makes or receives 5 telephone calls. What is the probability that this person is on the telephone for more than 45 minutes?

$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.2237$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.2596$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.3384$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.3975$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.4085$

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