An article in a magazine discussed the length of time till failure of a particular product. At the end of the product's lifetime, the time till failure is modeled using an exponential distribution with a mean of 500 thousand hours. In reliability jargon this is known as the "wear-out" distribution for the product. During its normal (useful) life, assume the product's time till failure is uniformly distributed over the range 200 thousand to 1 million hours. Complete parts a through c. a. At the end of the product's lifetime, find the probability that the product fails before 600 thousand hours. (Round to four decimal places as needed.)
An article in a magazine discussed the length of time till failure of a particular product. At the end of the product's lifetime, the time till failure is modeled using an exponential distribution with a mean of 500 thousand hours. In reliability jargon this is known as the "wear-out" distribution for the product. During its normal (useful) life, assume the product's time till failure is uniformly distributed over the range 200 thousand to 1 million hours. Complete parts a through c. a. At the end of the product's lifetime, find the probability that the product fails before 600 thousand hours. (Round to four decimal places as needed.)
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.
Chapter1: Functions
Section1.EA: Extended Application Using Extrapolation To Predict Life Expectancy
Problem 6EA
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Question
![An article in a magazine discussed the length of time till failure of a particular product.
At the end of the product's lifetime, the time till failure is modeled using an exponential
distribution with a mean of 500 thousand hours. In reliability jargon this is known as
the "wear-out" distribution for the product. During its normal (useful) life, assume the
product's time till failure is uniformly distributed over the range 200 thousand to 1
million hours. Complete parts a through c.
a. At the end of the product's lifetime, find the probability that the product fails before
600 thousand hours.
(Round to four decimal places as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbea0901b-9b71-43dc-90d5-d9e10ed3de89%2Fbb41d148-7cd8-4859-ad2e-636be4db3379%2F0xwa5uj_processed.png&w=3840&q=75)
Transcribed Image Text:An article in a magazine discussed the length of time till failure of a particular product.
At the end of the product's lifetime, the time till failure is modeled using an exponential
distribution with a mean of 500 thousand hours. In reliability jargon this is known as
the "wear-out" distribution for the product. During its normal (useful) life, assume the
product's time till failure is uniformly distributed over the range 200 thousand to 1
million hours. Complete parts a through c.
a. At the end of the product's lifetime, find the probability that the product fails before
600 thousand hours.
(Round to four decimal places as needed.)
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Follow-up Questions
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Follow-up Question
Please do part c)
![An article in a magazine discussed the length of time till failure of a particular product. At the end of the product's lifetime, the time till failure is modeled using an exponential distribution with a mean
of 500 thousand hours. In reliability jargon this is known as the "wear-out" distribution for the product. During its normal (useful) life, assume the product's time till failure is uniformly distributed over
the range 200 thousand to 1 million hours. Complete parts a through c.
a. At the end of the product's lifetime, find the probability that the product fails before 600 thousand hours.
0.6988 (Round to four decimal places as needed.)
b. During its normal (useful) life, find the probability that the product fails before 600 thousand hours.
0.5000 (Round to four decimal places as needed.)
c. Show that the probability of the product failing before 855 thousand hours is approximately the same for both the normal (useful) life distribution and the wear-out distribution.
The probability of the product failing before 855 thousand hours for the normal (useful) life distribution is
(Round to four decimal places as needed.)](https://content.bartleby.com/qna-images/question/bea0901b-9b71-43dc-90d5-d9e10ed3de89/4d126fcc-1938-4bc5-adb2-257f04c601fd/fjr52oj_thumbnail.png)
Transcribed Image Text:An article in a magazine discussed the length of time till failure of a particular product. At the end of the product's lifetime, the time till failure is modeled using an exponential distribution with a mean
of 500 thousand hours. In reliability jargon this is known as the "wear-out" distribution for the product. During its normal (useful) life, assume the product's time till failure is uniformly distributed over
the range 200 thousand to 1 million hours. Complete parts a through c.
a. At the end of the product's lifetime, find the probability that the product fails before 600 thousand hours.
0.6988 (Round to four decimal places as needed.)
b. During its normal (useful) life, find the probability that the product fails before 600 thousand hours.
0.5000 (Round to four decimal places as needed.)
c. Show that the probability of the product failing before 855 thousand hours is approximately the same for both the normal (useful) life distribution and the wear-out distribution.
The probability of the product failing before 855 thousand hours for the normal (useful) life distribution is
(Round to four decimal places as needed.)
Solution
Follow-up Question
Please do part b)
![An article in a magazine discussed the length of time till failure of a particular product. At the end of the product's lifetime, the time till failure is modeled using an exponential distribution with a mean
of 500 thousand hours. In reliability jargon this is known as the "wear-out" distribution for the product. During its normal (useful) life, assume the product's time till failure is uniformly distributed over
the range 200 thousand to 1 million hours. Complete parts a through c.
a. At the end of the product's lifetime, find the probability that the product fails before 600 thousand hours.
0.6988 (Round to four decimal places as needed.)
b. During normal (useful) life, find the probability that the product fails before 600 thousand hours.
(Round to four decimal places as needed.)](https://content.bartleby.com/qna-images/question/bea0901b-9b71-43dc-90d5-d9e10ed3de89/b1f983c9-eb8d-4976-9810-d58ea3a281e9/3pieap8_thumbnail.png)
Transcribed Image Text:An article in a magazine discussed the length of time till failure of a particular product. At the end of the product's lifetime, the time till failure is modeled using an exponential distribution with a mean
of 500 thousand hours. In reliability jargon this is known as the "wear-out" distribution for the product. During its normal (useful) life, assume the product's time till failure is uniformly distributed over
the range 200 thousand to 1 million hours. Complete parts a through c.
a. At the end of the product's lifetime, find the probability that the product fails before 600 thousand hours.
0.6988 (Round to four decimal places as needed.)
b. During normal (useful) life, find the probability that the product fails before 600 thousand hours.
(Round to four decimal places as needed.)
Solution
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