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Solved: The analysis of results from a leaf transmutation

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

Solution for problem 147E 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 147E

Problem 147E

The analysis of results from a leaf transmutation experiment (turning a leaf into a petal) is summarized by the type of transformation completed:

A naturalist randomly selects three leaves from this set without replacement. Determine the following probabilities.

(a) Exactly one has undergone both types of transformations.

(b) At least one has undergone both transformations.

(c) Exactly one has undergone one but not both transformations.

(d) At least one has undergone at least one transformation.

Step-by-Step Solution:

Solution :

Step 1 of 4:

Given the leaf transformation experiment table is given below.

                           Total Textural

Transformation

Yes

No

Total Color

Yes

243

26

Transformation

No

13

18

Here, N, n and K is

N= 243+26+13+18 = 300

The sample size n is randomly selected.

So n= 3.

K= 243 (both type of transformations)

Then the probability mass function is

P(X=x) =

Where, N=300, n=3 and K=243.

Our goal is:

a). We need to find the probability that exactly one leaf has undergone both types of transformations.

b). We need to find the probability that at least one leaf has undergone both types of transformations.

c). We need to find the probability that exactly one has undergone one but not both transformations.

d). We need to find the probability that at least one has undergone at least one transformation.

a). The probability that exactly one leaf has undergone both types of transformations is

P(X=1) =

P(X=1) =

P(X=1) =

P(X=1) =

P(X=1) = 0.0870

Therefore, the probability that exactly one leaf has undergone both types of transformations is 0.0870.


Step 2 of 4

Chapter 3.8, Problem 147E is Solved
Step 3 of 4

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

The answer to “The analysis of results from a leaf transmutation experiment (turning a leaf into a petal) is summarized by the type of transformation completed: A naturalist randomly selects three leaves from this set without replacement. Determine the following probabilities.(a) Exactly one has undergone both types of transformations.(b) At least one has undergone both transformations.(c) Exactly one has undergone one but not both transformations.(d) At least one has undergone at least one transformation.” is broken down into a number of easy to follow steps, and 71 words. The full step-by-step solution to problem: 147E from chapter: 3.8 was answered by , our top Statistics solution expert on 07/28/17, 07:57AM. 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. Since the solution to 147E from 3.8 chapter was answered, more than 4419 students have viewed the full step-by-step answer. This full solution covers the following key subjects: transformations, undergone, both, least, Transformation. This expansive textbook survival guide covers 97 chapters, and 2005 solutions.

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Solved: The analysis of results from a leaf transmutation