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 1109 and a standard deviation of 196. Scores on the ACT test are normally distributed with a mean of 20.9 and a standard deviation of 4.4. 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 33-percentile, find the actual SAT score.
SAT score = ?
Then Round answer to a whole number.

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

If a student gets an SAT score of 1579, find the equivalent ACT score.
ACT score = ?
Then Round answer to 1 decimal place.

Answer 1

Given that, scores on the SAT test are normally distributed with a mean of 1109 and a standard deviation of 196.

Let X ~ Normal (1109, 196)

Scores on the ACT test are normally distributed with a mean of 20.9 and a standard deviation of 4.4.

Let Y ~ Normal (20.9, 4.4)

a) We want to find, the value of x such that, P(X < x) = 0.33

Therefore, required SAT score = 1022.76

Now, we wanf to find, the value of y for Z = -0.44

y = (-0.44 * 4.4) + 20.9

=> y = -1.936 + 20.9

=> y = 18.964

=> y ≈ 19.0

Therefore, required ACT score = 19.0

b) z-score for x = 1579

Z = (1579 - 1109) / 196 = 470 / 196 = 2.40

We want to find, the value of y for Z = 2.40

y = (2.40 * 4.4) + 20.9

=> y = 10.56 + 20.9

=> y = 31.46

=> y = 31.5

Therefore, required ACT score = 31.5