Given : A standardized exam's scores are normally distributed. In a recent year, the mean test score was 1530 and the standard deviation was 316.
i.e. [tex]\mu=1530[/tex] and [tex]\sigma=316[/tex] .
Usual values have a z-score between -1.96 and 1.96.
The test scores of four students selected at random are 1930, 1250, 2250, and 1420.
Formula for z : [tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x= 1930 , [tex]z=\dfrac{1930-1530}{316}\approx1.27[/tex]
The z-score for 1930 is 1.27.
For x= 1250 , [tex]z=\dfrac{1250-1530}{316}\approx-0.89[/tex]
The z-score for 1250 is -0.89.
For x=2250 , [tex]z=\dfrac{2250-1530}{316}\approx2.28[/tex]
The z-score for 1250 is 2.28 .
For x= 1420 , [tex]z=\dfrac{1420-1530}{316}\approx-0.35[/tex]
The z-score for 1250 is -0.35 .
Since all the z-values lie between -1.96 and 1.96 except 2.28 corresponding to x=2250.
Thus , the z-score corresponding to x=2250 is unusual.
