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The article “Reliability-Based Service-Life Assessment of

Probability and Statistics for Engineers and the Scientists | 9th Edition | ISBN: 9780321629111 | Authors: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye ISBN: 9780321629111 32

Solution for problem 89E Chapter 3

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Probability and Statistics for Engineers and the Scientists | 9th Edition | ISBN: 9780321629111 | Authors: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Problem 89E

The article “Reliability-Based Service-Life Assessment of Aging Concrete Structures” (J. Structural Engr., 1993: 1600–1621) suggests that a Poisson process can be used to represent the occurrence of structural loads over time. Suppose the mean time between occurrences of loads is .5 year. a.? ow many loads can be expected to occur during a 2- year period? b.? ?What is the probability that more than five loads occur during a 2-year period? c. ?How long must a time period be so that the probability of no loads occurring during that period is at most .1?

Step-by-Step Solution:

Answer: Step 1 of 1 Suppose the mean time between occurrences of loads is 0.5 year. Here, T exp() and E(T ) = 1/ = 0.5. Therefore = 2. a. Let Y be the number of occurrences during a 2-year period, then t = 4 and Y = X2 Poisson(4). So E(Y ) = 4 Hence, expected number of loads to occur during a 2- year period is 4. b. The probability that more than five loads occur during a 2-year period is given below, Apply a poisson model with = 4 P(X > 5) = 1 P(X 5) = 1 F(5; 4)[Using excel function “=poisson(5,4,TRUE)”] = 1 - 0.7851 = 0.2149. Therefore, the probability that more than five loads occur during a 2-year period is 0.2149. 2t 0 e (2t) c. We know that P(X = 0t = 0! 2t e 0.1 = 2t ln(0.1) t 1.1513years. Hence, the probability of no loads occurring during that period is at most 0.1 is 1.1513 years.

Step 2 of 1

Chapter 3, Problem 89E is Solved
Textbook: Probability and Statistics for Engineers and the Scientists
Edition: 9
Author: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye
ISBN: 9780321629111

This textbook survival guide was created for the textbook: Probability and Statistics for Engineers and the Scientists, edition: 9. Probability and Statistics for Engineers and the Scientists was written by and is associated to the ISBN: 9780321629111. This full solution covers the following key subjects: loads, period, during, occur, structural. This expansive textbook survival guide covers 18 chapters, and 1582 solutions. Since the solution to 89E from 3 chapter was answered, more than 758 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 89E from chapter: 3 was answered by , our top Statistics solution expert on 05/06/17, 06:21PM. The answer to “The article “Reliability-Based Service-Life Assessment of Aging Concrete Structures” (J. Structural Engr., 1993: 1600–1621) suggests that a Poisson process can be used to represent the occurrence of structural loads over time. Suppose the mean time between occurrences of loads is .5 year. a.? ow many loads can be expected to occur during a 2- year period? b.? ?What is the probability that more than five loads occur during a 2-year period? c. ?How long must a time period be so that the probability of no loads occurring during that period is at most .1?” is broken down into a number of easy to follow steps, and 94 words.

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