Explanation Given information: The amount of time required to serve a customer at a bank has an exponential density function with mean 3 minutes. That is E ( X ) = 3 . Explanation: Let X be a random variable which denotes the amount of time required to serve a customer at a bank. Since X is an exponential random variable, its density function is f ( x ) = k e − k x ; x ≥ 0 , for some k > 0 and E ( X ) = 1 k . Given expected value is E ( X ) = 3 . Compare E ( X ) = 1 k with E ( X ) = 3 . This indicates 1 k = 3 . ⇒ k = 1 3 Therefore, the density function f ( x ) = k e − k x becomes f ( x ) = 1 3 e − ( 1 / 3 ) x ; x ≥ 0 Use the below formula tofind Pr ( X < 2 )

12th Edition

ISBN: 9780137590810

Author: Larry J. Goldstein, David C. Lay, David I. Schneider, Nakhle H. Asmar, William Edward Tavernetti

Publisher: PEARSON

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Chapter 12.4, Problem 7E

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The probability that the customer is served in less than 2 minutes; that is, find Pr(X<2), where the amount of time required to serve a customer at a bank has an exponential density function with mean 3 minutes.

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Chapter 12.4, Problem 6E

Chapter 12.4, Problem 8E

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The probability that the customer is served in less than 2 minutes; that is, find Pr ( X < 2 ) , where the amount of time required to serve a customer at a bank has an exponential density function with mean 3 minutes.

Solution Summary: The author explains that the probability that a customer is served in less than 2 minutes is 0.4866.

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The probability that the customer is served in less than 2 minutes; that is, find Pr(X<2), where the amount of time required to serve a customer at a bank has an exponential density function with mean 3 minutes.

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Chapter 12 Solutions

The probability that the customer is served in less than 2 minutes; that is, find Pr ( X &lt; 2 ) , where the amount of time required to serve a customer at a bank has an exponential density function with mean 3 minutes.

Solution Summary: The author explains that the probability that a customer is served in less than 2 minutes is 0.4866.

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The probability that the customer is served in less than 2 minutes; that is, find Pr(X<2), where the amount of time required to serve a customer at a bank has an exponential density function with mean 3 minutes.

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Chapter 12 Solutions

The probability that the customer is served in less than 2 minutes; that is, find Pr ( X < 2 ) , where the amount of time required to serve a customer at a bank has an exponential density function with mean 3 minutes.