Use a symbolic integration utility to find the required probability using the exponential density function 1-t/A. (t) = e-A, [0, ). The time (in years) until failure of a component in a machine is exponentially distributed with A = 3.6. A manufacturer has a large number of these machines and plans to replace the components in all the machines during regularly scheduled maintenance periods. How much time should elapse between maintenance periods if at least 95% of the components are to remain working throughout the period? (Round your answer to three decimal places.) yr

A First Course in Probability (10th Edition)
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Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Use a symbolic integration utility to find the required probability using the exponential density function
1-t/A.
(t) = e-A, [0, ).
The time (in years) until failure of a component in a machine is exponentially distributed with A
= 3.6. A manufacturer has a large number of these machines and plans to replace
the components in all the machines during regularly scheduled maintenance periods. How much time should elapse between maintenance periods if at least 95% of the
components are to remain working throughout the period? (Round your answer to three decimal places.)
yr
Transcribed Image Text:Use a symbolic integration utility to find the required probability using the exponential density function 1-t/A. (t) = e-A, [0, ). The time (in years) until failure of a component in a machine is exponentially distributed with A = 3.6. A manufacturer has a large number of these machines and plans to replace the components in all the machines during regularly scheduled maintenance periods. How much time should elapse between maintenance periods if at least 95% of the components are to remain working throughout the period? (Round your answer to three decimal places.) yr
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