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Rom4ik [11]
3 years ago
9

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

Mathematics
1 answer:
OverLord2011 [107]3 years ago
3 0
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(\dfrac{X-1028}{92}\le\dfrac{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

\dfrac{k-1028}{92}=\hat k\implies k\approx92(0.7722)+1028=1099.04\approx1099
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