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A fiber-spinning process currently produces a fiber whose

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

Solution for problem 17E Chapter 4.5

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 17E

A fiber-spinning process currently produces a fiber whose strength is normally distributed with a mean of 75 N/m2. The minimum acceptable strength is 65 N/m2.

a.Ten percent of the fiber produced by the current method fails to meet the minimum specification. What is the standard deviation of fiber strengths in the current process?

b. If the mean remains at 75 N/m2, what must the standard deviation be so that only 1 % of the fiber will fail to meet the specification?

c. If the standard deviation is 5 N/m2, to what value must the mean be set so that only 1% of the fiber will fail to meet the specification?

Step-by-Step Solution:

Answer:

Step 1 of 3:

(a)

In this question, given that the 10% of the fiber produced by the current method fails to meet the minimum specification. we are asked to find the standard deviation of fiber strengths in the fiber-spinning process.

Fiber strength is normally distributed with a mean of 75.

The minimum acceptable strength is 65.

Let  be the strength of the fiber.

The proportion of strengths that are less than 65 is 0.10 means 10th percentile of strength.

From the  table, the closest area to 0.1 is 0.1014, and corresponding   is .

Let  be the required standard deviation.

The z-score of 65 is,

 z =  =

=

Hence the standard deviation of fiber strengths is 0.78125 .

Step 2 of 3:

(b)

In this question, we are asked to find the standard deviation be so that only 1 % of the fiber will fail to meet the specification. 

If mean remains same.

From the  table, the closest area to 0.01 is 0.0099, and corresponding   is .

The z-score of 65 is,

 z =  =

=

Hence the standard deviation of fiber strengths is 0.4.291 .

Step 3 of 3

Chapter 4.5, Problem 17E is Solved
Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

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