Question 1191023: Data from a state indicate that scores on the SAT test are normally distributed with a mean of 1044 and a standard deviation of 194. Scores on the ACT test are normally distributed with a mean of 20.9 and a standard deviation of 4.4. 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 51 percentile, find the actual SAT score. Round answer to a whole number.
SAT score =
What would be the equivalent ACT score for this student? Round answer to 1 decimal place.
ACT score =
If a student gets an SAT score of 1451, find the equivalent ACT score. Round answer to 1 decimal place.
ACT score =
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! z=(x-mean)/sd
0.51 or 51st percentile is z=0.025
z*sd=0.025*194=4.85=x-mean
the score x for SAT is therefore 1048.85=1049
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The ACT score is about 1/50 th of the SAT score, so the ACT score is going to change about 0.1
z=0.025
z*sd=0.11
the ACT score will be 21.01 or 21.0
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z=(1451-1044)/194=2.098
for ACT, z*sd=9.23 or 9.2
The ACT score will be 30.1
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