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?

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.

Chapter13: Probability And Calculus

Section13.CR: Chapter 13 Review

Problem 60CR

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