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Chapter 7: Q. 2.19 (page 491)

When people order books from a popular online source, they are shipped in boxes.

Suppose that the mean weight of the boxes is 1.5 pounds with a standard deviation of 0.3 pound, the mean weight of the packing material is 0.5pound with a standard deviation of 0.1 pound, 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

b. 2.60

c. 3.02

d. 3.40

e. 9.10

Short Answer

Expert verified

(c) The standard deviation of the total weight of the boxes that are shipped from this source is3.02.

Step by step solution

01

Given Information

Given,

ver(total)=var(A)+var(B)+var(C)

A is the Weight of boxes

B is the weight of packing

C is the weight of boxes

Below is the Formula used:

SD=variance
02

Explanation of the correct option

Consider that,

ver(total)=0.32+0.12+32=9.1SD=9.1=3.02

Therefore, the correct option is (c)

03

Explanation of the incorrect option

(a) The standard deviation of the total weight of the boxes that are shipped from this source will not be1.84.

(b) The standard deviation of the total weight of the boxes that are shipped from this source will not be2.60.

(d) The standard deviation of the total weight of the boxes that are shipped from this source will not be 3.40

(e) The standard deviation of the total weight of the boxes that are shipped from this source will not be9.10.

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Section II: Free Response Show all your work. Indicate clearly the methods you use, because you will be graded on the correctness of your methods as well as on the accuracy and completeness of your results and explanations.

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