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Section I: Multiple Choice Choose the best answer for each question. When people order

Chapter 7, Problem AP2.19

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QUESTION:

Section I: Multiple Choice Choose the best answer for each question.

When people order books from a popular online source, they are shipped in standard-sized boxes. Suppose that the mean weight of the boxes is 1.5 pounds with a standard deviation of 0.3 pounds, the mean weight of the packing material is 0.5 pounds with a standard deviation of 0.1 pounds, and the mean weight of the books shipped is 12 pounds with a standard deviation of 3 pounds.

Assuming that the weights are independent, what is the standard deviation of the total weight of the boxes that are shipped from this source?

(a) 1.84         (c) 3.02         (e) 9.10

(b) 2.60         (d) 3.40

Questions & Answers

QUESTION:

Section I: Multiple Choice Choose the best answer for each question.

When people order books from a popular online source, they are shipped in standard-sized boxes. Suppose that the mean weight of the boxes is 1.5 pounds with a standard deviation of 0.3 pounds, the mean weight of the packing material is 0.5 pounds with a standard deviation of 0.1 pounds, and the mean weight of the books shipped is 12 pounds with a standard deviation of 3 pounds.

Assuming that the weights are independent, what is the standard deviation of the total weight of the boxes that are shipped from this source?

(a) 1.84         (c) 3.02         (e) 9.10

(b) 2.60         (d) 3.40

ANSWER:

Step 1 of 3

The goal of the problem is to determine the standard deviation of the total weight of the boxes being shipped.

We need to consider that the total weight comes from different boxes whose weight follows different distributions with its own mean and standard deviation as well. The standard deviation is just the square root of variance both measuring the spread of values.

Based on the Variance-Sum Law, if there are any two independent variables  and , and , then the variance of  would be equal to:

Extending this law to several variables, then, the variance of the sum of  independent variables would just be the sum of their respective variances.

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