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.

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

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

= 60 + 90

= 150

Therefore, The mean perimeter is 150 .

Step3 of 3:

b).

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

=

=

= 0.4472

Therefore, The standard deviation of the perimeter is 0.4472.

Conclusion:

a).The mean perimeter is 150 .

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