The four sides of a picture frame consist of two pieces

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

ISBN: 9780073401331 38

Solution for problem 9E Chapter 2.5

Statistics for Engineers and Scientists | 4th Edition

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Problem 9E

The four sides of a picture frame consist of two pieces selected from a population whose mean length is 30 cm with standard deviation 0.1 cm, and two pieces selected from a population whose mean length is 45 cm with standard deviation 0.3 cm.

a. Find the mean perimeter.

b. Assuming the four pieces are chosen independently, find the standard deviation of the perimeter.

Step-by-Step Solution:

Step 1 of 3

Solution 9E

Step1 of 3:

We have four sides of a picture frame and it consist of two pieces selected from a population whose mean length is 30 cm and standard deviation is 0.1cm.Two pieces selected from a population whose mean length is 45 cm with standard deviation 0.3 cm.

That is ${\mu{}}_{1}=30\ cm,\ {\sigma{}}_{1}=0.1\ cm\ and\ {n}_{1}=2\$

${\mu{}}_{2}=45\ cm,\ {\sigma{}}_{2}=0.3\ cm\ and\ {n}_{2}=2$

Here our goal is:

a).We need to find the mean perimeter.

b). We need to find the standard deviation of the perimeter by Assuming the four pieces are chosen independently.

Step2 of 3:

a).

The mean perimeter is given by

${(n}_{1}\times{}{\mu{}}_{1})+{(n}_{2}\times{}{\mu{}}_{2})=(2\times{}30)+(2\times{}45)$

= 60 + 90

= 150 $cm$

Therefore, The mean perimeter is 150 $cm$ .

Step3 of 3:

b).

Let us assume that four pieces are chosen independently, then the standard deviation of the perimeter is given by

$\sqrt{({n}_{1}\times{}{\sigma{}}_{1}^{2})+({n}_{2}\times{}{\sigma{}}_{2}^{2})}=\sqrt{[2\times{}{(0.1)}_{\ }^{2}]+[2\times{}{(0.3)}_{\ }^{2}]}$

= $\sqrt{0.02+0.18}$

= $\sqrt{0.2}$

= 0.4472 $cm$

Therefore, The standard deviation of the perimeter is 0.4472 $cm$ .

Conclusion:

a).The mean perimeter is 150 $cm$ .

b).The standard deviation of the perimeter is 0.4472 $cm$ .

Step 2 of 3

Chapter 2.5, Problem 9E is Solved

Step 3 of 3

Textbook: Statistics for Engineers and Scientists

Edition: 4

Author: William Navidi

ISBN: 9780073401331

This full solution covers the following key subjects: mean, standard, pieces, deviation, Find. 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. The full step-by-step solution to problem: 9E from chapter: 2.5 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. The answer to “?The four sides of a picture frame consist of two pieces selected from a population whose mean length is 30 cm with standard deviation 0.1 cm, and two pieces selected from a population whose mean length is 45 cm with standard deviation 0.3 cm.a. Find the mean perimeter.b. Assuming the four pieces are chosen independently, find the standard deviation of the perimeter.” is broken down into a number of easy to follow steps, and 62 words. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. Since the solution to 9E from 2.5 chapter was answered, more than 1487 students have viewed the full step-by-step answer.

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The four sides of a picture frame consist of two pieces

Solution for problem 9E Chapter 2.5

Chapter 2.5, Problem 9E is Solved

Textbook: Statistics for Engineers and Scientists

Edition: 4

Author: William Navidi

ISBN: 9780073401331

Other solutions

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