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Suppose that when a transistor of a certain type is subjected to an accelerated life test, the lifetime x (in weeks) has a gamma distribution with mean 28 weeks and standard deviation 14 weeks. (a) What is the probability that a transistor will last between 14 and 28 weeks? (Round your answer to three decim places.) (b) What is the probability that a transistor will last at most 28 weeks? (Round your answer to three decimal places Is the median of the lifetime distribution less than 282 Why or why not?

Suppose that when a transistor of a certain type is subjected to an accelerated life test, the lifetime x (in weeks) has a gamma distribution with mean 28 weeks and standard deviation 14 weeks. (a) What is the probability that a transistor will last between 14 and 28 weeks? (Round your answer to three decim places.) (b) What is the probability that a transistor will last at most 28 weeks? (Round your answer to three decimal places Is the median of the lifetime distribution less than 282 Why or why not?

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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Suppose that when a transistor of a certain type is subjected to an accelerated life test, the lifetime X (in weeks) has a gamma distribution with mean 28 weeks and standard deviation 14 weeks. (a) What is the probability that a transistor will last between 14 and 28 weeks? (Round your answer to three decimal places.) (b) What is the probability that a transistor will last at most 28 weeks? (Round your answer to three decimal places.) Is the median of the lifetime distribution less than 28? Why or why not? The median is-Select--- | 28, since P(X < ) = .5. (c) What is the 99th percentile of the lifetime distribution? (Round your answer to the nearest whole number.) (d) Suppose the test will actually be terminated after t weeks. What value of t is such that only 0.5% of all transistors would still be operating at termination? (Round your answer to the nearest whole number.) t = weeks You may need to use the appropriate table in the Appendix of Tables to answer this question.
Transcribed Image Text:Suppose that when a transistor of a certain type is subjected to an accelerated life test, the lifetime X (in weeks) has a gamma distribution with mean 28 weeks and standard deviation 14 weeks. (a) What is the probability that a transistor will last between 14 and 28 weeks? (Round your answer to three decimal places.) (b) What is the probability that a transistor will last at most 28 weeks? (Round your answer to three decimal places.) Is the median of the lifetime distribution less than 28? Why or why not? The median is-Select--- | 28, since P(X < ) = .5. (c) What is the 99th percentile of the lifetime distribution? (Round your answer to the nearest whole number.) (d) Suppose the test will actually be terminated after t weeks. What value of t is such that only 0.5% of all transistors would still be operating at termination? (Round your answer to the nearest whole number.) t = weeks You may need to use the appropriate table in the Appendix of Tables to answer this question.
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