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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Answers

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\copyright \ 2013

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4 responses

  1. Could you please post the process of how you arrived at the answer?

    1. Palitha Sarukkali | Reply

      Please explain how you arrived a this answer

  2. can you help me how to solve this problem?

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