Chapter 1, Problem 1SE

A vendor converts the weights on the packages she sends out from pounds to kilograms (1 kg ≈ 2.2 lb).

1. a. How does this affect the mean weight of the packages?
2. b. How does this affect the standard deviation of the weights?

To determine

How the converted kilograms affect the mean weights of the packages.

Answer to Problem 1SE

The converted kilograms affects that the mean weights of the packages will be divided by 2.2.

Explanation of Solution

Given info:

A vendor converts the weights on the packages sends out from pounds to kilograms $\left(1\text{kg}\approx \text{2}\text{.2 lb}\right)$.

Calculation:

The mean defines that the center or average of the data and it is calculated by the sum of the numbers in the sample and divided by total numbers.

Also, if a constant is multiply (or divided) to each sample item then the sample means multiply (or divided) by the same constant.

Thus, it can be concluded that the converted kilograms affect the mean weights of the packages will be divided by 2.2.

To determine

How the converted kilograms affect the standard deviation of the weights.

Answer to Problem 1SE

The converted kilograms affects that the standard deviation will be divided by 2.2.

Explanation of Solution

Calculation:

The standard deviation defines the quantity and it measures the degree of spread in a sample.

Also, if a constant is multiply (or divided) to each sample item then the sample standard deviation multiply (or divided) by the same constant.

Thus, it can be concluded that the converted kilograms affect that the standard deviation will be divided by 2.2.