Question

use the following distribution to complete parts (a) through (d) below.

1, 4, 7, 12, 11

a) compute the mean and standard deviation of the distribution.

the mean is 7.

the standard deviation is 4.64.
(round to the nearest hundredth as needed.)

b) multiply each number in the distribution by 3 and compute the mean and the standard deviation of this new distribution.

the mean is 21.

the standard deviation is 13.91.
(round to the nearest hundredth as needed.)

c) multiply each number in the original distribution by 9 and compute the mean and the standard deviation of this new distribution.

the mean is

Explanation:

Calculate the mean of the new distribution

Using the Linear Transformations of Data and Mean Calculation knowledge points

$$ \mu_{\text{new}} = 9 \times \mu_{\text{original}} = 9 \times 7 = 63 $$

Calculate the standard deviation of the new distribution

Using the Linear Transformations of Data and Sample Standard Deviation knowledge points

$$ \sigma_{\text{new}} = 9 \times \sigma_{\text{original}} \approx 9 \times 4.6368 = 41.73 $$

Answer:

c) Multiply each number in the original distribution by 9 and compute the mean and the standard deviation of this new distribution.

The mean is <blank>63</blank>.

The standard deviation is <blank>41.73</blank>.
(Round to the nearest hundredth as needed.)