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 1013 and a standard deviation of 197. Scores on the ACT test are normally distributed with a mean of 19.3 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 39-percentile, find the actual SAT score.
SAT score =
Round answer to a whole number.

What would be the equivalent ACT score for this student?
ACT score =
Round answer to 1 decimal place.

If a student gets an SAT score of 1368, find the equivalent ACT score.
ACT score =
Round answer to 1 decimal place.

Explanation / Answer

Ans:

39th percentile for SAT score:

P(Z<=z)=0.39

z=-0.279

x=1013-0.279*197=958

For equivalent ACT score:

x=19.3-0.279*5.2=17.8

For SAT score of 1368:

z=(1368-1013)/197=1.8

Equivalent ACT score,x=19.3+1.8*5.2=28.7

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