There are two major tests of readiness for college: the ACT and the SAT. ACT sco
ID: 3204708 • 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 1286 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
SAT scores
Mean ( u ) =1026
Standard Deviation ( sd )=209
Normal Distribution = Z= X- u / sd ~ N(0,1)
P(X < 1286) = (1286-1026)/209
= 260/209= 1.244
= P ( Z <1.244) From Standard Normal Table
= 0.8933
Joe scores 1286 on the SAT and he is at 89.33% perccentage
ACT score is for 89.33% is as below,
P ( Z < x ) = 0.8933
Value of z to the cumulative probability of 0.8933 from normal table is 1.244
P( x-u/s.d < x - 20.9/4.8 ) = 0.8933
That is, ( x - 20.9/4.8 ) = 1.24
--> x = 1.24 * 4.8 + 20.9 = 26.8712
the score that equaliant to Joe score at ACT score is 26.8712