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A new surgical procedure is successful with a probability

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

Problem 44E 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 44E

A new surgical procedure is successful with a probability of p. Assume that the operation is performed five times and the results are independent of one another. What is the probability that

a all five operations are successful if p = .8?

b exactly four are successful if p = .6?

c less than two are successful if p = .3?

Step-by-Step Solution:

Step 1 of 3</p>

a) We have to find the probability of all operations are successful if p=0.8

And q=1-0.8

          =0.2

Given that the operation is performed 5 times

Then n=5

Let X be the no.of successful operations

Then

The pmf of binomial distribution is

P(all operations are successful)=P(X=5)

                                                 

                                                  =0.32768

Hence the probability of all operations are successful is 0.32768

Step 2 of 3</p>

b) We have to find the probability of exactly 4 operations are successful if p=0.6

And q=1-0.6

          =0.4

Here

P(Exactly 4 are successful)=P(X=4)

                                           =

                                           =0.2592

Hence the probability of exactly 4 operations are successful is 0.2592

Step 3 of 3

Chapter 3, Problem 44E is Solved
Textbook: Mathematical Statistics with Applications
Edition: 7
Author: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer
ISBN: 9780495110811

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A new surgical procedure is successful with a probability

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