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 admittance. Scores on the SAT test are normally distributed with a mean of 1089 and a standard deviation of 199. Scores on the ACT test are normally distributed with a mean of 20.4 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 21-percentile, find the actual SAT score. Round answer to a whole number.

What would be the equivalent ACT score for this student? Round answer to 1 decimal place.

If a student gets an SAT score of 1567, find the equivalent ACT score. Round answer to 1 decimal place.

Answer 1

Data given for SAT scores:

Mean, m = 1089

Standard Deviation, S = 199

At p = 0.21, we have:

z = -0.806

Using formula:

z = (X-m)/S

So,

X = z*S + m = (-0.806)*199 + 1089 = 928.61

Data given for ACT scores:

Mean, m = 20.4

Standard Deviation, S = 5.1

With z = -0.806, the corresponding ACT score is:

X = z*S + m = (-0.806)*5.1 + 20.4 = 16.29

Now,

When SAT score is 1567, the corresponding z-value is:

z = (X-m)/S = (1567-1089)/199 = 2.4

With z = 2.4, the corresponding ACT score is:

X = z*S + m = (2.4)*5.1 + 20.4 = 32.64