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)$1.84$
(b) $2.60$

(c) $3.02$

(d) $3.40$

(e)$9.10$

Short answer

The standard deviation of the total weight of the boxes that are shipped from this source is $3.02$. So, the option (c) is correct.

Step-by-step solution

Given information

Let, 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.

Explanation

The variance of three boxes could be determined by:

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

The Standard deviation is need to square to get the variances.
$$\begin{gathered} \mathrm{var}\left(\text{total}\right)={0.3}^2+{0.1}^2+3^2=9.1 \\ =9.1 \end{gathered}$$

Now, the standard deviation could be calculated as follows:

Standard deviation $=\sqrt{9.1}$

Then, take out the square root.

$=3.02$

Hence, the standard deviation of three boxes is $3.02$.

So, the correct answer is option (c).