Question

Suppose you have a normally distributed set of data pertaining to a standardized test. The mean score is 1050 and the standard deviation is 200. What is the z-score of 1300 point score?

Suppose you have a normally distributed set of data pertaining to a standardized test. The mean score is 1050 and the standard deviation is 200. What is the z-score of 1400 point score?

Answer 1

By the definition of Standard normal probability distribution,

" If X is a normally distributed random variable $\mu$ and $\sigma$ are respectively its mean and the standard deviation, then $z=\frac{X-\mu}{\sigma}$ is called the standard normal variable. "

Given that, "The normamally distributed set of data pertaining toa standardized test"

(1)

The mean score $\mu =1050$

Standard deviation $= \sigma =200$

To find the z-score of 1300 point score:

That is, $X=1300$

Then the z score is given by

$z=\frac{X- \mu}{\sigma}=\frac{1300-1050}{200}=\frac{250}{200}=1.25 \\ Then \\ z-score=1.25$

(2)

The mean score $\mu =1050$

Standard deviation $= \sigma =200$

To find the z-score of 1400 point score:

That is, $X=1400$

Then the z score is given by

$z=\frac{X- \mu}{\sigma}=\frac{1400-1050}{200}=\frac{350}{200}=1.75 \\ Then \\ z-score=1.75$