A study was conducted

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 1086 and a standard deviation of 197. Scores on the ACT test are normally distributed with a mean of 20.3 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 24-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 1283, find the equivalent ACT score.

ACT score = 

Round answer to 1 decimal place.

Answer 1

If a student gets an SAT score that is the 24-percentile, find the actual SAT score.

First you have to either use a chart or the invNorm function on your calculator to get the z score. Once you have the z score, you set it equal to (X-mu)/standard deviation. If you do this in your calculator it gives you the answer.

-.706=(X-1086)/197 or in calculator: InvNorm(.24,1086,197)

X = 946.86

SAT score = 947

Round answer to a whole number.

What would be the equivalent ACT score for this student?

-.71= (X-20.3)/4.9 or in calculator: InvNorm(.24,20.3,4.9)

X=16.84

ACT score = 16.8

Round answer to 1 decimal place.

If a student gets an SAT score of 1283, find the equivalent ACT score.

z=(1283-1086)/197

z= 1

So, 1 = (X-20.3)/4.9

X= 25.2

ACT score = 25.2

Round answer to 1 decimal place.