The time to failure, t, in hours, of a machine is often exponentially distributed with a probability density function f(t)= kekt, 0≤t<∞o, where k= and a is the average amount of time that will pass before a failure occurs. Suppose that the average amount of time that will pass before a failure occurs is 80 hr. What is the probability that a failure will occur in 58 hr or less?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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The probability is
(Round to four decimal places as needed.)
Transcribed Image Text:The probability is (Round to four decimal places as needed.)
The time to failure, t, in hours, of a machine is often exponentially distributed with a probability density function f(t)= kekt, 0≤t<∞o, where
1
a
and a is the average amount of time that will pass before a failure occurs. Suppose that the average amount of time that will pass before
a failure occurs is 80 hr. What is the probability that a failure will occur in 58 hr or less?
k=
Transcribed Image Text:The time to failure, t, in hours, of a machine is often exponentially distributed with a probability density function f(t)= kekt, 0≤t<∞o, where 1 a and a is the average amount of time that will pass before a failure occurs. Suppose that the average amount of time that will pass before a failure occurs is 80 hr. What is the probability that a failure will occur in 58 hr or less? k=
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