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Refer to Exercise 3.92. What is the probability that the

Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer ISBN: 9780495110811 47

Solution for problem 93E Chapter 3

Mathematical Statistics with Applications | 7th Edition

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Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer

Mathematical Statistics with Applications | 7th Edition

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Problem 93E

Problem 93E

Refer to Exercise 3.92. What is the probability that the third non-defective engine will be found

a on the fifth trial?

b on or before the fifth trial?

Reference

Ten percent of the engines manufactured on an assembly line are defective. If engines are randomly selected one at a time and tested, what is the probability that the first non-defective engine will be found on the second trial?

Step-by-Step Solution:

Solution

Step 1 of 2

a) We have to find the probability of finding 3rd non-defective engine in the fifth trial

Given that 10% of the engines are defective

And 90% of the engines are non defectives

Then p=0.9

And  q=1-0.9

           =0.1

The pmf of negative binomial distribution for n trials, given k success is

Here n=5

        k=3

         =(0.729)(0.01)

         =0.04374

Hence the probability of finding 3rd non-defective engine in the fifth trial is 0.04374


Step 2 of 2

Chapter 3, Problem 93E is Solved
Textbook: Mathematical Statistics with Applications
Edition: 7
Author: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer
ISBN: 9780495110811

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Refer to Exercise 3.92. What is the probability that the