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.

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JeanaShupp JeanaShupp · Answer 1 · 2019-08-19T13:40:22+02:00

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

Mean test score : [tex]\mu=1490 [/tex]

Standard deviation : [tex]\sigma=320[/tex]

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

z-score : [tex]z=\dfrac{x-\mu}{\sigma}[/tex]

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

For x= 1900

[tex]z=\dfrac{1900-1490}{320}\approx1.28[/tex]

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

For x= 1240

[tex]z=\dfrac{1240-1490}{320}\approx-0.78[/tex]

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

For x= 2190

[tex]z=\dfrac{2190-1490}{320}\approx2.19[/tex]

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

For x= 1240

[tex]z=\dfrac{1370-1490}{320}\approx-0.38[/tex]

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