SOLUTION: 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 are approximately Normal wi

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Question 1092414: 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 are approximately Normal with mean μ = 21.5 and standard deviation σ = 5.4. SAT scores are reported on a scale from 600 to 2400. The SAT scores are approximately Normal with mean μ = 1498 and standard deviation σ = 316.
What SAT scores make up the top 25% of all scores? (Round your answer to the nearest whole number.)
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
z for 75 th percentile is +0.675, so we want everything greater than z=0.675
z=(x-mean)/sd
0.675=(x-1498)/316
213.3=x-1498
x=1711.3
everything greater than a score of 1711 for SAT.
===============
0.675=(x-21.5)/5.4
3.645=x-21.5
x=25.1, everything greater than a score of 25 for ACT.