A system consists of five components is connected in series as shown below. As soon as one component fails, the entire system will fail. Assume that the components fail independently of one nother. a) Suppose that each of the first two components have lifetimes that are exponentially distributed with mean 91 weeks, and that each of the last three components have lifetimes that are exponentially distributed with mean 121 weeks. Find the probability that the system lasts at least 50 weeks. b) Now suppose that each component has a lifetime that is exponentially distributed with the same mean. What must that mean be (in years) so that 94% of all such systems lasts at least one year?

A system consists of five components is connected in series as shown below. As soon as one component fails, the entire system will fail. Assume that the components fail independently of one nother. a) Suppose that each of the first two components have lifetimes that are exponentially distributed with mean 91 weeks, and that each of the last three components have lifetimes that are exponentially distributed with mean 121 weeks. Find the probability that the system lasts at least 50 weeks. b) Now suppose that each component has a lifetime that is exponentially distributed with the same mean. What must that mean be (in years) so that 94% of all such systems lasts at least one year?

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.CR: Chapter 13 Review

Problem 61CR

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