Question

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 0.5 pound 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

c. 3.02

Step-by-step solution

Given Information

$ver\left(\text{total}\right)=var\left(A\right)+var\left(B\right)+var$(C)

A= Weight of boxes

B= weight of packing

C= weight of boxes

Formula used:

Explanation for correct option

$$\begin{gathered} ver\left(\text{total}\right)=0.3^2+0.1^2+3^2=9.1 \\ SD=\sqrt{9.1}=3.02 \end{gathered}$$

Hence, the correct option is (c)

Explanation for incorrect option

a. 1.84 is not the correct answer.

b. 2.60 is not the correct answer.

d. 3.40 is not the correct answer.

e. 9.10 is not the correct answer.