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# A complex electronic system is built with a certain number ISBN: 9780495110811 47

## Solution for problem 39E Chapter 3

Mathematical Statistics with Applications | 7th Edition

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Problem 39E

A complex electronic system is built with a certain number of backup components in its subsystems. One subsystem has four identical components, each with a probability of .2 of failing in less than 1000 hours. The subsystem will operate if any two of the four components are operating. Assume that the components operate independently. Find the probability that

a exactly two of the four components last longer than 1000 hours.

b the subsystem operates longer than 1000 hours.

Step-by-Step Solution:

Step 1 of 2:

Given 4 identical components are there in one subsystem.

Then the probability of 0.2 of failing in less than 1000 hours.

We assume that the components operate are independent.

Our goal is:

a). We need to find the probability that exactly two of the four components last longer than

1000 hours.

b). We need to find the probability that the subsystem operates longer than 1000 hours.

a).

Now we have to find the probability that exactly two of the four components last longer than 1000 hours.

Let Y is the number of components failing in less than 1000 hours.

Here Y is binomial with parameter n and p.

So n=4 and p=0.8 and

q=1-p

q=1-0.20

q=0.80

Therefore q=0.80.

Then the probability that exactly two of the four components last longer than 1000 hours is

The formula of the binomial is

P(Y) = Then, P(Y=2) is

P(Y=2)= P(Y=2)= P(Y=2)= P(Y=2)= 0.1536

Therefore, the probability that exactly two of the four components last longer than 1000 hours is 0.1536.

Step 2 of 2

##### ISBN: 9780495110811

The full step-by-step solution to problem: 39E from chapter: 3 was answered by , our top Statistics solution expert on 07/18/17, 08:07AM. This textbook survival guide was created for the textbook: Mathematical Statistics with Applications , edition: 7. The answer to “A complex electronic system is built with a certain number of backup components in its subsystems. One subsystem has four identical components, each with a probability of .2 of failing in less than 1000 hours. The subsystem will operate if any two of the four components are operating. Assume that the components operate independently. Find the probability thata exactly two of the four components last longer than 1000 hours.b the subsystem operates longer than 1000 hours.” is broken down into a number of easy to follow steps, and 76 words. Since the solution to 39E from 3 chapter was answered, more than 603 students have viewed the full step-by-step answer. Mathematical Statistics with Applications was written by and is associated to the ISBN: 9780495110811. This full solution covers the following key subjects: components, subsystem, Probability, operate, longer. This expansive textbook survival guide covers 32 chapters, and 3350 solutions.

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