A system consists of five components is connected in series as shown below. 5 2 As soon as one component fails, the entire system will fail. Assume that the components fail independently of one another. (a) Suppose that each of the first two components have lifetimes that are exponentially distributed with mean 109 weeks, and that each of the last three components have lifetimes that are exponentially distributed with mean 128 weeks. Find the probability that the system lasts at least 49 weeks. (b) Now suppose that each component has a lifetime that is exponentially distributed with the same mean. What must that mean be (in years) so that 97% of all such systems lasts at least one year?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
icon
Related questions
Question
Problem #7: A system consists of five components is connected in series as shown below.
5
As soon as one component fails, the entire system will fail. Assume that the components fail independently of
one another.
(a) Suppose that each of the first two components have lifetimes that are exponentially distributed with mean 109
weeks, and that each of the last three components have lifetimes that are exponentially distributed with mean
128 weeks. Find the probability that the system lasts at least 49 weeks.
(b) Now suppose that each component has a lifetime that is exponentially distributed with the same mean. What
must that mean be (in years) so that 97% of all such systems lasts at least one year?
Transcribed Image Text:Problem #7: A system consists of five components is connected in series as shown below. 5 As soon as one component fails, the entire system will fail. Assume that the components fail independently of one another. (a) Suppose that each of the first two components have lifetimes that are exponentially distributed with mean 109 weeks, and that each of the last three components have lifetimes that are exponentially distributed with mean 128 weeks. Find the probability that the system lasts at least 49 weeks. (b) Now suppose that each component has a lifetime that is exponentially distributed with the same mean. What must that mean be (in years) so that 97% of all such systems lasts at least one year?
Expert Solution
steps

Step by step

Solved in 3 steps with 6 images

Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Holt Mcdougal Larson Pre-algebra: Student Edition…
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL