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 20 weeks and standard deviation 10 weeks. (a) What is the probability that a transistor will last between 10 and 20 weeks? (Round your answer to three decimal places.) (b) What is the probability that a transistor will last at most 20 weeks? (Round your answer to three decimal places.) Is the median of the lifetime distribution less than 20? Why or why not? The median is less than 20, since P(X sÃ) = .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.) weeks
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 20 weeks and standard deviation 10 weeks. (a) What is the probability that a transistor will last between 10 and 20 weeks? (Round your answer to three decimal places.) (b) What is the probability that a transistor will last at most 20 weeks? (Round your answer to three decimal places.) Is the median of the lifetime distribution less than 20? Why or why not? The median is less than 20, since P(X sÃ) = .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.) weeks
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...
Related questions
Concept explainers
Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Question
100%
Please solve (c) & (d) only!
![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 20 weeks and standard deviation 10 weeks.
(a) What is the probability that a transistor will last between 10 and 20 weeks? (Round your answer to three decimal places.)
(b) What is the probability that a transistor will last at most 20 weeks? (Round your answer to three decimal places.)
Is the median of the lifetime distribution less than 20? Why or why not?
The median is less than
20, since P(X < D) = .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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc32f563a-6b55-4123-a4c3-1254c39a7403%2F34045a1c-9f92-4d27-848c-e8cc30fdf45c%2Fhkb1kdm_processed.png&w=3840&q=75)
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 20 weeks and standard deviation 10 weeks.
(a) What is the probability that a transistor will last between 10 and 20 weeks? (Round your answer to three decimal places.)
(b) What is the probability that a transistor will last at most 20 weeks? (Round your answer to three decimal places.)
Is the median of the lifetime distribution less than 20? Why or why not?
The median is less than
20, since P(X < D) = .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
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 6 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.Recommended textbooks for you
![A First Course in Probability (10th Edition)](https://www.bartleby.com/isbn_cover_images/9780134753119/9780134753119_smallCoverImage.gif)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
![A First Course in Probability](https://www.bartleby.com/isbn_cover_images/9780321794772/9780321794772_smallCoverImage.gif)
![A First Course in Probability (10th Edition)](https://www.bartleby.com/isbn_cover_images/9780134753119/9780134753119_smallCoverImage.gif)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
![A First Course in Probability](https://www.bartleby.com/isbn_cover_images/9780321794772/9780321794772_smallCoverImage.gif)