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Males and females are observed to react differently to a

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

Solution for problem 129E Chapter 2

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 129E

Problem 129E

Males and females are observed to react differently to a given set of circumstances. It has been observed that 70% of the females react positively to these circumstances, whereas only 40% of males react positively. A group of 20 people, 15 female and 5 male, was subjected to these circumstances, and the subjects were asked to describe their reactions on a written questionnaire. A response picked at random from the 20 was negative. What is the probability that it was that of a male?

Step-by-Step Solution:

Solution

Step 1 of 2

We have to find the probability of getting negative reaction that it is from male

Let M be the reaction from the male

Let F be the reaction from the female

Let N be the negative reaction

Given that

Probability of female reacts positively is 0.7

Probability of female reacts negatively is P(N/F)=1-0.7

                                                                              =0.3

Probability of male reacts positively is 0.4

Probability of male reacts negatively is P(N/M)=1-0.4

                                                                              =0.6

The no.of survey people is 20 in that 15 female and 5 male

Probability of female is P(F)=15/20

                                              =0.75

Probability of male is P(M)=5/20

                                              =0.25


Step 2 of 2

Chapter 2, Problem 129E is Solved
Textbook: Mathematical Statistics with Applications
Edition: 7
Author: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer
ISBN: 9780495110811

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Males and females are observed to react differently to a