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A 500-page book contains 250 sheets of paper. The

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

Solution for problem 2E Chapter 4.11

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 2E

A 500-page book contains 250 sheets of paper. The thickness of the paper used to manufacture the book has mean 0.08 mm and standard deviation 0.01 mm.

a. What is the probability that a randomly chosen book is more than 20.2 mm thick (not including the covers)?

b. What is the 10th percentile of book thicknesses?

c. Someone wants to know the probability that a randomly chosen page is more than 0.1 mm thick. Is enough information given to compute this probability? If so, compute the probability. If not, explain why not.

Step-by-Step Solution:

Answer:

Step 1 of 3:

(a)

In this question, we are asked to find the probability that a randomly chosen book is more than 20.2  thick (not including the covers).

A - page book contains sheets of paper.

Thickness of paper has mean  and standard deviation .

Let denote the thickness of the 250 sheets of paper.

We need to find

Now the sample size is , which is a large sample.

Then according to Central Limit Theorem,

Let  be a simple random sample from a population with mean

and variance .

Let  =  be the total thickness.

Hence  can be approximately normal distributed.

CLT specifies that and  for sum of the sample items.

Hence we achieve,

Mean

 

Variance

= 250

 =

Standard deviation

Therefore we can write,

Now we will calculate the  score because our distribution is approximately normal.

thus the  score of 20.2  is

=

=

 = 1.265

From the z table, the area to the left of  is 0.8962.

Hence the area to the right is

 = 1 - the area to the left of

 = 1 - 0.8962

 = 0.1038

Hence the probability that a randomly chosen book is more than 20.2  thick is 0.1038.

Step 2 of 3

Chapter 4.11, Problem 2E is Solved
Step 3 of 3

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

The full step-by-step solution to problem: 2E from chapter: 4.11 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. The answer to “A 500-page book contains 250 sheets of paper. The thickness of the paper used to manufacture the book has mean 0.08 mm and standard deviation 0.01 mm.a. What is the probability that a randomly chosen book is more than 20.2 mm thick (not including the covers)?________________b. What is the 10th percentile of book thicknesses?________________c. Someone wants to know the probability that a randomly chosen page is more than 0.1 mm thick. Is enough information given to compute this probability? If so, compute the probability. If not, explain why not.” is broken down into a number of easy to follow steps, and 89 words. This full solution covers the following key subjects: Book, Probability, thick, compute, Randomly. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. Since the solution to 2E from 4.11 chapter was answered, more than 2359 students have viewed the full step-by-step answer.

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