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Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger
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Solved: Calls to the help line of a large computer

Chapter 4, Problem 144E

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QUESTION:

Problem 144E

Calls to the help line of a large computer distributor follow a Poisson distribution with a mean of 20 calls per minute. Determine the following:

(a) Mean time until the one-hundredth call

(b) Mean time between call numbers 50 and 80

(c) Probability that three or more calls occur within 15 seconds

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QUESTION:

Problem 144E

Calls to the help line of a large computer distributor follow a Poisson distribution with a mean of 20 calls per minute. Determine the following:

(a) Mean time until the one-hundredth call

(b) Mean time between call numbers 50 and 80

(c) Probability that three or more calls occur within 15 seconds

ANSWER:

Solution :

Step 1 of 3:

Let X denotes the time (in min) until the 100th call.

Then X follows a gamma distribution with , and r=100.

Our goal is:

a). We need to find the mean time until the one-hundredth call.

b). We need to find the mean time between call numbers 50 and 80.

d). We need to find the probability of three or more calls occurs within 15 seconds.

a). The expectation of X = expected time until 100th call

Expectation of X = E(X)

Expectation of X =

Expectation of X =  

Expectation of X = 5

Therefore, the mean time until the one-hundredth call is 5.

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