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) The standard deviation of the total weight of the boxes that are shipped from this source is$3.02$.

Step-by-step solution

Given Information

Given,

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

A is the Weight of boxes

B is the weight of packing

C is the weight of boxes

Below is the Formula used:

$SD=\sqrt{\text{variance}}$

Explanation of the correct option

Consider that,

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

Therefore, the correct option is (c)

Explanation of the incorrect option

(a) The standard deviation of the total weight of the boxes that are shipped from this source will not be$1.84$.

(b) The standard deviation of the total weight of the boxes that are shipped from this source will not be$2.60.$

(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 be$9.10$.