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The time to failure (in days) of a starter motor in a vehicle is modeled as a Weibull distribution with ō = 2000, B = 2.7. (a) What is the probability that a starter motor fails within 4 years? Round your answer to three decimal places (e.g. 98.765). P(X< 4 x 365) = (b) What is the probability a motor fails in less than 5 years given that is has lasted more than two years? Round your answer to three decimal places (e.g. 98.765). P(X<5 x 365 | X > 2× 365) = (c) Compare your answer in the previous part to the probability that a motor fails in less than three years and comment on whether the lack of memory property applies to this distribution. Round your answer to three decimal places (e.g. 98.765). P(X<3 x 365) = The lack of memory property to this distribution. (d) Suppose that the time to failure (in days) of a new starter motor follows a Weibull distribution with 6-3000, B -3.2 and that lifetime is defined as the time exceeded by 99% of motors. Which motor has a longer lifetime?

The time to failure (in days) of a starter motor in a vehicle is modeled as a Weibull distribution with ō = 2000, B = 2.7. (a) What is the probability that a starter motor fails within 4 years? Round your answer to three decimal places (e.g. 98.765). P(X< 4 x 365) = (b) What is the probability a motor fails in less than 5 years given that is has lasted more than two years? Round your answer to three decimal places (e.g. 98.765). P(X<5 x 365 | X > 2× 365) = (c) Compare your answer in the previous part to the probability that a motor fails in less than three years and comment on whether the lack of memory property applies to this distribution. Round your answer to three decimal places (e.g. 98.765). P(X<3 x 365) = The lack of memory property to this distribution. (d) Suppose that the time to failure (in days) of a new starter motor follows a Weibull distribution with 6-3000, B -3.2 and that lifetime is defined as the time exceeded by 99% of motors. Which motor has a longer lifetime?

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 time to failure (in days) of a starter motor in a vehicle is modeled as a Weibull distribution with ō = 2000, B = 2.7. (a) What is the probability that a starter motor fails within 4 years? Round your answer to three decimal places (e.g. 98.765). P(X< 4 x 365) = (b) What is the probability a motor fails in less than 5 years given that is has lasted more than two years? Round your answer to three decimal places (e.g. 98.765). P(X<5 x 365 | X > 2×365) (c) Compare your answer in the previous part to the probability that a motor fails in less than three years and comment on whether the lack of memory property applies to this distribution. Round your answer to three decimal places (e.g. 98.765). P(X<3 x 365) = The lack of memory property to this distribution. (d) Suppose that the time to failure (in days) of a new starter motor follows a Weibull distribution with 6-3000, B =3.2 and that lifetime is defined as the time exceeded by 99% of motors. Which motor has a longer lifetime?
Transcribed Image Text:The time to failure (in days) of a starter motor in a vehicle is modeled as a Weibull distribution with ō = 2000, B = 2.7. (a) What is the probability that a starter motor fails within 4 years? Round your answer to three decimal places (e.g. 98.765). P(X< 4 x 365) = (b) What is the probability a motor fails in less than 5 years given that is has lasted more than two years? Round your answer to three decimal places (e.g. 98.765). P(X<5 x 365 | X > 2×365) (c) Compare your answer in the previous part to the probability that a motor fails in less than three years and comment on whether the lack of memory property applies to this distribution. Round your answer to three decimal places (e.g. 98.765). P(X<3 x 365) = The lack of memory property to this distribution. (d) Suppose that the time to failure (in days) of a new starter motor follows a Weibull distribution with 6-3000, B =3.2 and that lifetime is defined as the time exceeded by 99% of motors. Which motor has a longer lifetime?
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