There are two major tests of readiness for college, the ACT and the SAT. ACT sco
ID: 3398215 • 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 for more than 1 million students in a recent high school graduating class was roughly normal with mean = 15.6 and standard deviation = 3.9. SAT scores are reported on a scale from 400 to 1600. The SAT scores for 1.4 million students in the same graduating class were roughly normal with mean = 999 and standard deviation = 190. Jose scores 927 on the SAT. Assuming that both tests measure the same thing, what score on the ACT is equivalent to Jose's SAT score?
Explanation / Answer
This is a observation from large ovserved data which is normally distributed random variables.
so z for noramally distributed ramdom variables =(observaed value-mean)/Standard Deviation
Jose Z score in Sat =(927-999)/190 =-0.3789
So jose ACT socore equivalent to this Sat score is =15.6+(-0.3789*3.9)=14.122