There are two major tests of readiness for college, the ACT and the SAT. ACT sco
ID: 3125541 • 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 are approximately Normal with mean = 21.5 and standard deviation = 5.4. SAT scores are reported on a scale from 600 to 2400. The SAT scores are approximately Normal with mean = 1509 and standard deviation = 321.
Maria scores 15 on the ACT. Assuming that both tests measure the same thing, what score on the SAT is equivalent to Maria's ACT score? (Round your answer to a whole number.)
Explanation / Answer
As
z = (x-u)/sigma
Then for Maria,
z(Maria) = (15 - 21.5)/5.4 = -1.203703704
Hence, as they have equal z score, and
x = u + z*sigma
Then for the SAT,
x = 1509 + (-1.203703704)*321 = 1122.61 = 1123 [ANSWER]