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 admittance. Scores on the SAT test are normally distributed with a mean of 1112 and a standard deviation of 200. Scores on the ACT test are normally distributed with a mean of 21 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 20-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 1512, find the equivalent ACT score.
ACT score =
Round answer to 1 decimal place.

Explanation / Answer

z score for 20th percentile = -0.84

Hence,

Actual SAT score = 1112 - 0.84*200 = 944

Equivalent ACT score = 21 - 0.84*5.2 = 16.6

z score for 1512 = (1512 - 1112)/200 = 2

Hence,

Equivalent ACT score = 21 + 2*5.2 = 31.4

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