Question

If the mean weight of all students in a class is 165 pounds with a variance of 234.09 square pounds, what is the z-value associated with a student whose weight is 140 pounds?

Answer 1

Answer:

$Z = -1.63$

Step-by-step explanation:

The z-score measures how many standard deviation a score X is above or below the mean.

it is given by the following formula:

$Z = \frac{X - \mu}{\sigma}$

In which

$\mu$ is the mean, $\sigma$ is the standard deviation

In this problem, we have that:

Mean weight of all students in a class is 165 pounds, so $\mu = 165$

Variance of 234.09 square pounds. The standard deviation is the square root of the variance. So $\sigma = \sqrt{234.09} = 15.3$

What is the z-value associated with a student whose weight is 140 pounds?

Z when X = 140. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{140 - 165}{15.3}$

$Z = -1.63$