The time between successive calls to a corporate office is exponentially distributed with a mean of 10 minutes. Assume that the times between successive calls are independent of each other. Thus, the calls arrive according to a Poisson process. a. If four nonoverlapping20 minutes intervals are selected, what is the probability that none of these intervals contains any call? b. What is the probability that the first occurrence in which the time between

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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The time between successive calls to a corporate office is exponentially distributed with a mean of 10 minutes. Assume that the times between successive calls are independent of each other. Thus, the calls arrive according to a Poisson process.

a. If four nonoverlapping20 minutes intervals are selected, what is the probability that none of these intervals contains any call?

b. What is the probability that the first occurrence in which the time between two calls exceeds 10 minutes is betweenthe fourth andthe fifth calls?

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