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Statistics / Statistics for Engineers and Scientists 4 / Chapter 4.3 / Problem 13E

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

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The number of defective components produced by a certain

Chapter 4, Problem 13E

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QUESTION:

The number of defective components produced by a certain process in one day has a Poisson distribution with mean 20. Each defective component has probability 0.60 of being repairable.

a. Find the probability that exactly 15 defective components are produced.

b. Given that exactly 15 defective components are produced, find the probability that exactly 10 of them are repairable.

c. Let \(N\) be the number of defective components produced, and let \(X\) be the number of them that are repairable. Given the value of \(N\), what is the distribution of \(X\)?

d. Find the probability that exactly 15 defective components are produced, with exactly 10 of them being repairable.

Equation Transcription:

$N$

$X$

Text Transcription:

N

X

Questions & Answers

QUESTION:

The number of defective components produced by a certain process in one day has a Poisson distribution with mean 20. Each defective component has probability 0.60 of being repairable.

a. Find the probability that exactly 15 defective components are produced.

b. Given that exactly 15 defective components are produced, find the probability that exactly 10 of them are repairable.

c. Let \(N\) be the number of defective components produced, and let \(X\) be the number of them that are repairable. Given the value of \(N\), what is the distribution of \(X\)?

d. Find the probability that exactly 15 defective components are produced, with exactly 10 of them being repairable.

Equation Transcription:

$N$

$X$

Text Transcription:

N

X

ANSWER:

Solution

Step 1of 5

Here given that the no.of defective components produced by process in one day has a poisson distribution with mean 20

So, $\lambda{}$ =20

The probability of the component is reparable is 0.6

So, p=0.6

Let N is no. of components produced by process

Here N $\sim{}$ poisson(20)

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