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Suppose that lesions are present at 5 sites among 50 in a

Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger ISBN: 9781118539712 55

Solution for problem 155E Chapter 3.8

Applied Statistics and Probability for Engineers | 6th Edition

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Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger

Applied Statistics and Probability for Engineers | 6th Edition

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Problem 155E

Suppose that lesions are present at 5 sites among 50 in a patient. A biopsy selects 8 sites randomly (without replacement).

(a) What is the probability that lesions are present in at least one selected site?

(b) What is the probability that lesions are present in two or more selected sites?

(c) Instead of eight sites, what is the minimum number of sites that need to be selected to meet the following objective? The probability that at least one site has lesions present is greater than or equal to 0.9.

Step-by-Step Solution:

Step 1 of 4:

The lesions are present at 5 sites among 50 in a patient.

A biopsy selects 8 sites randomly without replacement.

We have to find the probability that lesions are present in at least one selected site.We have to find the probability that lesions are present in two or more selected sites.We have to find the minimum number of sites that need to be selected to meet the object that the probability that at least one site has lesions present is greater than or equal to 0.9.

Step 2 of 4:

Let X be the number of lesions in patients.

Given population size, N= 50.

Sample, n = 8.

The number of patients that lesions are present in the population, K= 5.

From the given information, it is clear that X~ Hypergeometric distribution.

                                              P(X=k) =        x[ 0, n+K-N,..., ,min(n,K)]

                                             P(X=k) =  

           

(a)

The probability that lesions are present in at least one selected site.

                                           P(X) = 1- P(X=0)

                                                 

                                                          = 1-

                                                          = 1-

                                       = 1- 0.4014

                                                          = 0.5986

Therefore, the probability that lesions are present in at least one selected site is 0.5986.

Step 3 of 4

Chapter 3.8, Problem 155E is Solved
Step 4 of 4

Textbook: Applied Statistics and Probability for Engineers
Edition: 6
Author: Douglas C. Montgomery, George C. Runger
ISBN: 9781118539712

Since the solution to 155E from 3.8 chapter was answered, more than 318 students have viewed the full step-by-step answer. The answer to “Suppose that lesions are present at 5 sites among 50 in a patient. A biopsy selects 8 sites randomly (without replacement).(a) What is the probability that lesions are present in at least one selected site?(b) What is the probability that lesions are present in two or more selected sites?(c) Instead of eight sites, what is the minimum number of sites that need to be selected to meet the following objective? The probability that at least one site has lesions present is greater than or equal to 0.9.” is broken down into a number of easy to follow steps, and 87 words. Applied Statistics and Probability for Engineers was written by and is associated to the ISBN: 9781118539712. This full solution covers the following key subjects: sites, lesions, Present, Probability, selected. This expansive textbook survival guide covers 97 chapters, and 2005 solutions. This textbook survival guide was created for the textbook: Applied Statistics and Probability for Engineers , edition: 6. The full step-by-step solution to problem: 155E from chapter: 3.8 was answered by , our top Statistics solution expert on 07/28/17, 07:57AM.

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