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Chapter 7: Q. 19 (page 463)

When people order books from a popular online source, they are shipped in standard-sized boxes. Suppose that the mean weight of the boxes is1.5pounds with a standard deviation of 0.3pounds, the mean weight of the packing material is 0.5pounds with a standard deviation of 0.1 pounds, and the mean weight of the books shipped is12 pounds with a
standard deviation of3 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

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

01

Given information

Let, the mean weight of the boxes is 1.5pounds with a standard deviation of 0.3pounds, the mean weight of the packing material is 0.5pounds with a standard deviation of 0.1pounds, and the mean weight of the books shipped is 12pounds with a standard deviation of 3 pounds.

02

Explanation

The variance of three boxes could be determined by:

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

The Standard deviation is need to square to get the variances.
var(total)=0.32+0.12+32=9.1=9.1

Now, the standard deviation could be calculated as follows:

Standard deviation =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).

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