There are two major tests of readiness for college: the ACT and the SAT. ACT sco
ID: 3053396 • Letter: T
Question
There are two major tests of readiness for college: the ACT and the SAT. ACT scores are reported on a scale from 1 to 36. The distribution of ACT scores in recent years has been roughly Normal with mean µ = 20.9 and standard deviation s = 4.8. SAT scores are reported on a scale from 400 to 1600. SAT scores have been roughly Normal with mean µ = 1026 and standard deviation s = 209. Joe scores 1265 on the SAT. Assuming that both tests measure the same thing, what score (±1) on the ACT is equivalent to Joe's SAT score?
Explanation / Answer
For finding equivalent score, we may convert the SAT score in test to z score and use this z score to find out corresponding Z score. Z score measures how many standard deviations from mean, the raw score is at.
Z = (X - µ)/s
Z score of Joes SAT score = (1265 - 1026)/209)
= 1.14
Let A be Joe's ACT score corresponding to z score of 1.14
(A - µ)/s = 1.14
(A - 20.9)/4.8 = 1.14
A = 26.37
The ACT is equivalent to Joe's SAT score = 26.37