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Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 4 - Problem 15se
Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 4 - Problem 15se

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# Thicknesses of shims are normally distributed with mean

ISBN: 9780073401331 38

## Solution for problem 15SE Chapter 4

Statistics for Engineers and Scientists | 4th Edition

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Problem 15SE

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:

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 2

##### ISBN: 9780073401331

Since the solution to 15SE from 4 chapter was answered, more than 1169 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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