The coefficient of variation is 20%
The lower limit is 9 and the upper limit is 21
<h3 /><h3>How to calculate the coefficient of variation</h3>
Given the following parameters
- Sample mean "x" = 15
- standard deviation 's" = 3
The coefficient of variation is expressed as:
coefficient of variation = s/x * 100
coefficient of variation = 3/15 * 100
coefficient of variation = = 20%
Hence the coefficient of variation is 20%
The formula for the Chebyshev interval is given as:
![(x- 3k, x + 3k)](https://tex.z-dn.net/?f=%28x-%203k%2C%20x%20%2B%203k%29)
Get the value of k using the formula below:
![0.75=1-\frac{1}{k^2}\\ 0.25 = \frac{1}{k^2} \\k^2= \frac{1}{0.25} \\k = 2](https://tex.z-dn.net/?f=0.75%3D1-%5Cfrac%7B1%7D%7Bk%5E2%7D%5C%5C%200.25%20%3D%20%5Cfrac%7B1%7D%7Bk%5E2%7D%20%5C%5Ck%5E2%3D%20%5Cfrac%7B1%7D%7B0.25%7D%20%5C%5Ck%20%3D%202)
Get the required interval
![(15- 3(2), 15 + 3(2))\\(9,21)](https://tex.z-dn.net/?f=%2815-%203%282%29%2C%2015%20%2B%203%282%29%29%5C%5C%289%2C21%29)
Hence the lower limit is 9 and the upper limit is 21
Learn more on confidence intervals here: brainly.com/question/15712887