There are two major tests of readiness for college: the ACT and the SAT. ACT sco
ID: 3204662 • 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 1273 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
ans=
z = (X - Mean)/SD
X = Mean + (z*SD)
z-value corresponding to X = 1273 on the SAT is
z = (1273 - 1026)/209 = + 1.18 approximately
X-value corresponding to z = + 1.18 on ACT is
X = 20.9 + (1.18*4.8) = 25.69