Question

A standardized​ exam's scores are normally distributed. In a recent​ year, the mean test score was 14901490 and the standard deviation was 320320. The test scores of four students selected at random are 19001900​, 12401240​, 21902190​, and 13701370. Find the​ z-scores that correspond to each value and determine whether any of the values are unusual.

Answer 1

Answer with explanation:

Given : A standardized​ exam's scores are normally distributed.

Mean test score : $\mu=1490$

Standard deviation : $\sigma=320$

Let x be the random variable that represents the scores of students .

z-score : $z=\dfrac{x-\mu}{\sigma}$

We know that generally , z-scores lower than -1.96 or higher than 1.96 are considered unusual .

For x= 1900

$z=\dfrac{1900-1490}{320}\approx1.28$

Since it lies between -1.96 and 1.96 , thus it is not unusual.

For x= 1240

$z=\dfrac{1240-1490}{320}\approx-0.78$

Since it lies between -1.96 and 1.96 , thus it is not unusual.

For x= 2190

$z=\dfrac{2190-1490}{320}\approx2.19$

Since it is greater than 1.96 , thus it is unusual.

For x= 1240

$z=\dfrac{1370-1490}{320}\approx-0.38$

Since it lies between -1.96 and 1.96 , thus it is not unusual.