Scholastic Aptitude Test (SAT) scores are normally distributed with a mean of 500 points and a standard deviation of 100 points. Suppose you take the SAT and several weeks later you receive a letter telling you that your results on the math portion of the test were in the 80th percentile.

Recalling that SAT scores are always expressed as multiples of 10, how many points did you get on the test?

A.600

B.85

C.690

D.580

E.550

You basically want to find the score at which the cumulative distribution function is 0.8. If F(z) is the CDF of the normal distribution, then you have

F^-1(0.8) = (x-500)/100

0.8416 = (x-500)/100

584.16 = x

So the closest score is 580.