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 1039 and a standard deviation of 198. Scores on the ACT test are normally distributed with a mean of 22.9 and a standard deviation of 5.1. 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 79-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 1475, find the equivalent ACT score. ACT score =

Round answer to 1 decimal place.

Answer 1

We are given here that:

a) From standard normal tables, we have:
P(Z < 0.806) = 0.79

Therefore the 79^th percentile SAT score is obtained here as:
= Mean + 0.806*Std Dev
= 1039 + 0.806*198
= 1198.588

therefore 1199 is the required 79^th percentile SAT score here.

b) Now equivalent ACT score is computed in a similar way as:
= Mean + 0.806*Std Dev
= 22.9 + 0.806*5.1
= 27.0106

Therefore 27.0 is the required 79^th percentile ACT score here.

c) For a SAT score of 1475, the equivalent ACT score is computed here as:

Therefore 34.1 is the required equivalent score here.