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.

Question

Scores on the SAT test are normally distributed with a mean of 1109 and a standard deviation of 204. Scores on the ACT test are normally distributed with a mean of 19.5 and a standard deviation of 4.7. 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 22-percentile, find the actual SAT score.

What would be the equivalent ACT score for this student?

If a student gets an SAT score of 1313, find the equivalent ACT score.

Answer 1

SAT mean=1109 and stnddev=204

ACT mean=19.5 and stnddev=4.7

Prob(z < Z) = 0.22

then

Z = -0.772193214

by reverse table lookup (Normal.inverse)

The SAT score is -0.772193214 * 204 + 1109 = 951.472584344

The ACT score is -0.772193214 *4.7 + 19.5 = 15.8706918942

For SAT score 1313, the z-score is (1313-1109)/204 = 1

The ACT Score is 1 * 4.7 + 19.5 = 4.7 + 19.5 = 24.2