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A cylindrical hole is drilled in a block, and a

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

Solution for problem 13E 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 13E

A cylindrical hole is drilled in a block, and a cylindrical piston is placed in the hole. The. clearance is equal to one-half the difference between the diameters of the hole and the piston. The diameter of the hole is normally distributed with mean 15 cm and standard deviation 0.025 cm, and the diameter of the piston is normally distributed with mean 14.88 cm and standard deviation 0.015 cm.

a. Find the mean clearance.

b. Find the standard deviation of the clearance.

c. What is the probability that the clearance is less than 0.05 cm?

d. Find the 25th percentile of the clearance.

e. Specifications call for the clearance to be between 0.05 and 0.09 cm. What is the probability that the clearance meets the specification?

f. It is possible to adjust the mean hole diameter. To what value should it be adjusted so as to maximize the probability that the clearance will be between 0.05 and 0.09 cm?

Step-by-Step Solution:

Answer:

Step 1 of 6:

(a)

In this question, we are asked to find the mean clearance.

Clearance is equal to one-half the difference between the diameters of the hole and the piston.

The diameter of the hole has mean 15 and standard deviation .

The diameter of the piston has mean 14.88 and standard deviation

The diameter of both hole and the piston are normally distributed.

Let  be the diameter of the hole and be the diameter of piston.

Then we can write and as,

If are independent random variables and are constants, then

Mean will be linear combinations of these variables, hence we can write,

…….(1)

Likewise for standard deviation, we can write,

  ………(2)

The clearance is given by,

C =

Hence the mean of clearance,

 (using equation 1)

0.06

Hence the mean of clearance is 0.06.


Step 2 of 6

Chapter 4.5, Problem 13E is Solved
Step 3 of 6

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

The full step-by-step solution to problem: 13E from chapter: 4.5 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. The answer to “A cylindrical hole is drilled in a block, and a cylindrical piston is placed in the hole. The. clearance is equal to one-half the difference between the diameters of the hole and the piston. The diameter of the hole is normally distributed with mean 15 cm and standard deviation 0.025 cm, and the diameter of the piston is normally distributed with mean 14.88 cm and standard deviation 0.015 cm.a. Find the mean clearance.________________b. Find the standard deviation of the clearance.________________c. What is the probability that the clearance is less than 0.05 cm?________________d. Find the 25th percentile of the clearance.________________e. Specifications call for the clearance to be between 0.05 and 0.09 cm. What is the probability that the clearance meets the specification?________________f. It is possible to adjust the mean hole diameter. To what value should it be adjusted so as to maximize the probability that the clearance will be between 0.05 and 0.09 cm?” is broken down into a number of easy to follow steps, and 153 words. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. This full solution covers the following key subjects: clearance, hole, mean, standard, Find. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. Since the solution to 13E from 4.5 chapter was answered, more than 1118 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4.

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