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Six tissues are extracted from an ivy plant infested by

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

Solution for problem 151E Chapter 2.6

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 151E

Problem 151E

Six tissues are extracted from an ivy plant infested by spider mites. The plant in infested in 20% of its area. Each tissue is chosen from a randomly selected area on the ivy plant.

(a) What is the probability that four successive samples show the signs of infestation?

(b) What is the probability that three out of four successive samples show the signs of infestation?

Step-by-Step Solution:

Answer

Step 1 of 2

(a)

Six tissues are extracted from an ivy plant infested by spider mites. The plant in infested in  of its area. Each tissue is chosen from a randomly selected area of the ivy plant.

we are asked to find the probability that four successive samples show the signs of infestation.

Let  denote an infested plant sample.

Let  denote the good plan sample.

We have given the probability that the ivy plant is infested is

Hence the probability that the plant is not infected or good is

The number of ways to obtain four consecutive samples showing the signs of the infestation is,

 

Hence the probability is,

Hence the probability that four successive samples show the signs of an infestation is


Step 2 of 2

Chapter 2.6, Problem 151E is Solved
Textbook: Applied Statistics and Probability for Engineers
Edition: 6
Author: Douglas C. Montgomery, George C. Runger
ISBN: 9781118539712

The full step-by-step solution to problem: 151E from chapter: 2.6 was answered by , our top Statistics solution expert on 07/28/17, 07:57AM. This full solution covers the following key subjects: plant, infested, signs, infestation, successive. This expansive textbook survival guide covers 97 chapters, and 2005 solutions. Since the solution to 151E from 2.6 chapter was answered, more than 1119 students have viewed the full step-by-step answer. Applied Statistics and Probability for Engineers was written by and is associated to the ISBN: 9781118539712. This textbook survival guide was created for the textbook: Applied Statistics and Probability for Engineers , edition: 6. The answer to “Six tissues are extracted from an ivy plant infested by spider mites. The plant in infested in 20% of its area. Each tissue is chosen from a randomly selected area on the ivy plant.(a) What is the probability that four successive samples show the signs of infestation?(b) What is the probability that three out of four successive samples show the signs of infestation?” is broken down into a number of easy to follow steps, and 63 words.

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Six tissues are extracted from an ivy plant infested by