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Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 4.2 - Problem 24e
Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 4.2 - Problem 24e

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# One design for a system requires the installation of two

ISBN: 9780073401331 38

## Solution for problem 24E Chapter 4.2

Statistics for Engineers and Scientists | 4th Edition

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Problem 24E

Problem 24E

One design for a system requires the installation of two identical components. The system will work if at least one of' the components works. An alternative design requires four of these components, and the system will work if at least two of the four components work. If the probability that a component works is 0.9,and  if the components function independently! Which  design has the greater probability of functioning?

Step-by-Step Solution:
Step 1 of 3

Solution 24E

Step1 of 3:

Let us consider a design in that a system requires the installation of two identical components. The system will work if at least one of' the components works.An alternative design requires four of these components, and the system will work if at least two of the four components work.

P(component works) = 0.90.

P(none works) = 1 - P(component works)

= 1 - 0.90

= 0.10

We need to check which design has the greater probability of functioning.

Step2 of 3:

Consider,

P(at least one work) = P(X > 1)

=

=

=  1 - 0.01

=  0.99

Hence, probability that at least one work is 0.99.

Step3 of 3:

Consider a four components design.

P(at least 2 works) = P(X > 2)

= 1 -

= 1 - {0.0001+0.0036}

= 1 - 0.0037

= 0.9963

Hence, probability that at least 2 works is 0.9963.

Conclusion:

From step 2 and step 3, we can say that the an alternative Design has the greater probability of functioning.

Step 2 of 3

Step 3 of 3

##### ISBN: 9780073401331

This full solution covers the following key subjects: components, system, work, Design, works. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. The full step-by-step solution to problem: 24E from chapter: 4.2 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. The answer to “One design for a system requires the installation of two identical components. The system will work if at least one of' the components works. An alternative design requires four of these components, and the system will work if at least two of the four components work. If the probability that a component works is 0.9,and if the components function independently! Which design has the greater probability of functioning?” is broken down into a number of easy to follow steps, and 68 words. Since the solution to 24E from 4.2 chapter was answered, more than 409 students have viewed the full step-by-step answer.

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