There are two major tests of readiness for college: the ACT and the SAT. ACT sco
ID: 3204707 • 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. The SAT scores that make up the top 26% of all scores range from to 1600. (Round your answer to the nearest whole number.)
Explanation / Answer
Mean ( u ) =1026
Standard Deviation ( sd )=209
Normal Distribution = Z= X- u / sd ~ N(0,1)
SAT scores that make up the top 26% of all scores range from to 1600 = P ( Z > x ) = 0.26
Value of z to the cumulative probability of 0.26 from normal table is 0.64
P( x-u/ (s.d) > x - 1026/209) = 0.26
That is, ( x - 1026/209) = 0.64
--> x = 0.64 * 209+1026 = 1160.387