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The national average SAT score is 1028. The standard deviation is 92. What is the 78th percentile score?

User Tmhalbert
by
8.2k points

1 Answer

4 votes
You're looking for the score
k such that


\mathbb P(X\le k)=0.78

First transform
X to the standard normal random variable.


\mathbb P(X\le k)=\mathbb P\left((X-1028)/(92)\le(k-1028)/(92)\right)=\mathbb P(Z\le \hat k)=0.78

Now 0.78 corresponds to a z-score of approximately
\hat k=0.7722, which means


(k-1028)/(92)=\hat k\implies k\approx92(0.7722)+1028=1099.04\approx1099
User Oksana Romaniv
by
8.6k points
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