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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?

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)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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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