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A shipment of 20 cameras includes 3 that are defective.

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

Solution for problem 108E 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 108E

Problem 108E

A shipment of 20 cameras includes 3 that are defective. What is the minimum number of cameras that must be selected if we require that P(at least 1 defective) ≥ .8?

Step-by-Step Solution:

Answer:

Step 1 of 1:

In this question, we need to find the minimum number of cameras  that must be selected if we require that

 

We can write above probability like this,

…….(1)

Let is defined as a number of defective cameras.

Here, random variable  follows a hypergeometric distribution, because we are selecting cameras from twenty cameras of which some are defectives and some are non-defectives.

A random variable is said to have a  hypergeometric probability distribution if and only if

           [

…………..(2)

Where  is an integer  subject to the restrictions  and

Here,  

Hence we can find the value of  by substituting the value of r from 4 to 8 into equation (1), and we will check the value of probability whether it is equal to 0.2 or not. Then we can conclude the minimum number of cameras .

i). If ,

ii). If ,

iii). If ,

iii). If ,

iv). If ,

……..(3)

Both the probability value of equation (1) and (3) are approximately equal.

Hence  is the minimum number that the probability .


Step 2 of 1

Chapter 3, Problem 108E is Solved
Textbook: Mathematical Statistics with Applications
Edition: 7
Author: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer
ISBN: 9780495110811

This textbook survival guide was created for the textbook: Mathematical Statistics with Applications , edition: 7. The full step-by-step solution to problem: 108E from chapter: 3 was answered by , our top Statistics solution expert on 07/18/17, 08:07AM. Since the solution to 108E from 3 chapter was answered, more than 449 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: cameras, defective, minimum, least, includes. This expansive textbook survival guide covers 32 chapters, and 3350 solutions. The answer to “A shipment of 20 cameras includes 3 that are defective. What is the minimum number of cameras that must be selected if we require that P(at least 1 defective) ? .8?” is broken down into a number of easy to follow steps, and 31 words.

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