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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.6: Exponential And Logarithmic Equations

Problem 64E

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.9 Guaranteed life of a machine
The lifetime in hours of a certain component of a machine has the continuous probability
density function
-x/1000 x ≥ 0.
f(x) =
"
1000
The machine contains five similar components, the lifetime of each having the above
distribution. The makers are considering offering a guarantee that not more than two of the
original components will have to be replaced during the first 1000 hours of use. Find the
probability that such a guarantee would be violated, assuming that the components wear out
independently, and that if a component does fail then the replacement used is of particularly
high quality and will certainly last for the 1000 hours.

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