There are two major tests of readiness for college the ACT a

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?

Solution

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