A study was conducted on students from a particular high school over the last 8

Question

A study was conducted on students from a particular high school over the last 8 years. The following information was found regarding standardized tests used for college admitance. Scores on the SAT test are normally distributed with a mean of 1111 and a standard deviation of 201. Scores on the ACT test are normally distributed with a mean of 20.1 and a standard deviation of 5.2. It is assumed that the two tests measure the same aptitude, but use different scales.

If a student gets an SAT score that is the 35-percentile, find the actual SAT score. SAT score =

What would be the equivalent ACT score for this student? ACT score =

If a student gets an SAT score of 1493, find the equivalent ACT score. ACT score =

Explanation / Answer

Z score corresponding to 45 percentile which can bewritten as 0.35 is -1.81

So the SAT score will be

Z= X-mu/sigma

-1.81= X-1111/201

-1.81*201= X-1111

-363.81= X-1111

SAT SCORE= X= 1111-363.81= 747.19

The equivalent ACT SCORE IS

Z= X-MU/SIGMA

-1.81= X-20.1/5.2

-1.81*5.2= X-20

-9.412= X-20

-9.412+20= X

ACT SCORE =X= 10.588= 10.6

If a student get SAT SCORE X= 1493 the corresponding ACT SCORE WILL BE

Z= X-MU/SIGMA

Z= 1493-1111/201

Z= 382/201= 1.90

ACT SCORE WILL BE

Z= X-MU/SIGMA

1.90= X-20.1/5.2

1.90*5.2= X-20

9.88= X-20

ACT SCORE= X= 29.88

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