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 1057 and a standard deviation of 203. Scores on the ACT test are normally distributed with a mean of 22.6 and a standard deviation of 4.9. 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 34-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 1341, find the equivalent ACT score.
ACT score =  
Round answer to 1 decimal place.

Answer 1

Solution:

For SAT scores , = 1057 ,   = 203

For ACT scores , = 22.6 ,   = 4.9

1) If a student gets an SAT score that is the 34-percentile

For 34th percentile ,

P(Z < z) = 0.34

But from z table , P(Z < -0.412) = 0.34

So , z = -0.412

Using z score formula

x = + (z * ) = 1057 + ( -0.412 * 203) = 972.958 = 973

SAT score = 973

2) What would be the equivalent ACT score for this student?

ACT score =    + (z * ) = 22.6 + ( -0.412 * 4.9) =  20.5812 = 20.6

ACT score = 20.6

3)If a student gets an SAT score of 1341

z score = (X - )/ = (1341 - 1057)/203 = 1.399

equivalent ACT score =   + (z * ) = 22.6 + ( 1.399 * 4.9) = 29.5

ACT score = 29.5