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Shafts manufactured for use in optical storage devices

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

Solution for problem 14E 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 14E

Shafts manufactured for use in optical storage devices have diameters that are normally distributed with mean μ = 0.652 cm and standard deviation σ = 0.003 cm. The specification for the shaft diameter is 0.650 ± 0.005 cm.

a. What proportion of the shafts manufactured by this process meet the specifications?

b. The process mean can be adjusted through calibration. If the mean is set to 0.650 cm, what proportion of that; shafts will meet specifications?

c. If the mean is set to 0.650 cm, what must the standard deviation be so that 99% of the shafts will meet specifications?

Step-by-Step Solution:

Answer:

Step 1 of 3:

(a)

In this question, we are asked to find the proportion of the shafts manufactured by this process meet the specifications.

Shafts manufactured for use in optical storage devices have diameters that are normally distributed with mean  and standard deviation .

The specification for the shaft diameter is .

Let  represent the diameter of a randomly chosen shaft.

We need to find .

Here we can write,

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

The z-score of 0.645 is z  =

The z-score of 0.655 is z  =

The area to the left of  =  is 0.0099,  and the area to the left of  =  is 0.8413.

The area between =  and  =  is 0.8413 − 0.0099 = 0.8314.

Therefore  = 0.8314.

Hence 83.14% of the diameters will meet the specification.


Step 2 of 3

Chapter 4.5, Problem 14E is Solved
Step 3 of 3

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

Since the solution to 14E from 4.5 chapter was answered, more than 2524 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 14E from chapter: 4.5 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. The answer to “Shafts manufactured for use in optical storage devices have diameters that are normally distributed with mean ? = 0.652 cm and standard deviation ? = 0.003 cm. The specification for the shaft diameter is 0.650 ± 0.005 cm.a. What proportion of the shafts manufactured by this process meet the specifications?________________b. The process mean can be adjusted through calibration. If the mean is set to 0.650 cm, what proportion of that; shafts will meet specifications?________________c. If the mean is set to 0.650 cm, what must the standard deviation be so that 99% of the shafts will meet specifications?” is broken down into a number of easy to follow steps, and 97 words. This full solution covers the following key subjects: shafts, mean, specifications, meet, proportion. 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.

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