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Thicknesses of shims are normally distributed with mean

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 15SE Chapter 4

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 15SE

Thicknesses of shims are normally distributed with mean 1.5 mm and standard deviation 0.2 mm. Three shims are stacked, one atop another.

a. Find the probability that the stack is more than 5 mm thick.

b. Find the 80th percentile of the stack thickness.

c. What is the minimum number of shims to be stacked so that the probability that the stack is more than 5 mm thick is at least 0.99?

Step-by-Step Solution:

Step 1 of 3:

We consider the 3 thickness are .

Then the population mean and the standard deviation is 0.2 mm.

Let Y be the thickness of stack.

So Y=.

Our goal is :

a). We need to find the probability that the stack is more than 5 mm thick.

b). We need to find the 80th percentile of the stack thickness.

c). We need to find the minimum number of shims to be stacked so that the probability that the

      stack is more than 5 mm thick is at least 0.99.

a).

Now we have to find the probability that the stack is more than 5 mm thick.

Here .

We know that the sample size n=3.

Then mean .

Therefore mean is 4.5.

Then standard deviation is .

Therefore the standard deviation is 0.3461.

Hence

Then the formula of the z-score is

z=

The z score 5 is

z=

z=

z=.

Therefore z=1.44

Now the probability that the stack is more than 5 mm thick.

P(X>5)=1-P(X<5)

P(X>5)=1-0.9251 (using area under the normal table)

P(X>5)=0.0749.

Therefore the probability that the stack is more than 5 mm thick is 0.0749.

 

Step 2 of 3:

b).

Now we have find the 80th percentile of the stack thickness.

The z score of the 80th percentile is

z=0.84.

Then the formula of the z score is

z=

0.84=

0.840.3461=- 4.5

0.2907=- 4.5

=0.2907+4.5

=4.79

Therefore the 80th percentile of the stack thickness is 4.79.

Step 2 of 2

Chapter 4, Problem 15SE is Solved
Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

Since the solution to 15SE from 4 chapter was answered, more than 934 students have viewed the full step-by-step answer. This full solution covers the following key subjects: Stack, shims, Find, stacked, thick. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. The full step-by-step solution to problem: 15SE from chapter: 4 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. The answer to “Thicknesses of shims are normally distributed with mean 1.5 mm and standard deviation 0.2 mm. Three shims are stacked, one atop another.a. Find the probability that the stack is more than 5 mm thick.________________b. Find the 80th percentile of the stack thickness.________________c. What is the minimum number of shims to be stacked so that the probability that the stack is more than 5 mm thick is at least 0.99?” is broken down into a number of easy to follow steps, and 69 words. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4.

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