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The length of time of calls made to a support helpline follows an exponential distribution with an average duration of 20 minutes so that λ = (a) What is the probability that a call to the helpline lasts less than 10 minutes? (b) What is the probability that a call to the helpline lasts more than 30 minutes? (c) What is the probability that a call lasts between 20 and 30 minutes? = 0.05. (Round your answer to four decimal places.

The length of time of calls made to a support helpline follows an exponential distribution with an average duration of 20 minutes so that λ = (a) What is the probability that a call to the helpline lasts less than 10 minutes? (b) What is the probability that a call to the helpline lasts more than 30 minutes? (c) What is the probability that a call lasts between 20 and 30 minutes? = 0.05. (Round your answer to four decimal places.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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The length of time of calls made to a support helpline follows an exponential distribution with an average duration of 20 minutes so that \(\lambda = \frac{1}{20} = 0.05\). (Round your answer to four decimal places.) (a) What is the probability that a call to the helpline lasts less than 10 minutes? \[ \_\_\_\_\_\_ \] (b) What is the probability that a call to the helpline lasts more than 30 minutes? \[ \_\_\_\_\_\_ \] (c) What is the probability that a call lasts between 20 and 30 minutes? \[ \_\_\_\_\_\_ \] (d) Tchebysheff's Theorem says that the interval \(20 \pm 2(20)\) should contain at least 75% of the population. What is the actual probability that the call times lie in this interval? \[ \_\_\_\_\_\_ \]
Transcribed Image Text:The length of time of calls made to a support helpline follows an exponential distribution with an average duration of 20 minutes so that \(\lambda = \frac{1}{20} = 0.05\). (Round your answer to four decimal places.) (a) What is the probability that a call to the helpline lasts less than 10 minutes? \[ \_\_\_\_\_\_ \] (b) What is the probability that a call to the helpline lasts more than 30 minutes? \[ \_\_\_\_\_\_ \] (c) What is the probability that a call lasts between 20 and 30 minutes? \[ \_\_\_\_\_\_ \] (d) Tchebysheff's Theorem says that the interval \(20 \pm 2(20)\) should contain at least 75% of the population. What is the actual probability that the call times lie in this interval? \[ \_\_\_\_\_\_ \]
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