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

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 1117 and a standard deviation of 194. Scores on the ACT test are normally distributed with a mean of 21.9 and a standard deviation of 3.8. 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 77-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 1544, find the equivalent ACT score. 

ACT score =  

Round answer to 1 decimal place.

Answer 1

To be in the 77-percentile need the z value that gives probability of 0.77.

Going to the standard normal probabilities table 0.77 results in z equal to 0.74.

z value is calculated by the sample score minus the mean divided by the standard deviation.

z = (x - µ)/sigma. 0.74 = (x - 1117)/194. Solving for x yields x = 0.74 times 194 + 1117

x = 1,260.6

Rounding to the nearest whole number gives the student's SAT score = 1261

The same process is used for the ACT score. 0.74 = (x - µ)/sigma. This time µ = 21.9 and sigma = 3.8

This gives the new equation 0.74 = (x - 21.9)/3.8. Solving for x yields x = 0.74 times 3.8 + 21.9

x = 24.71

Rounding to the to 1 decimal place gives the student's ACT score = 24,7