Question

Consider a set of 7500 scores on a national test whose score is known to be distributed normally with a mean of 510 and a standard deviation of 85. About how many scores greater than 600 would we expect to find?

Answer 1

$\mathbb P(X>600)=\mathbb P\left(\dfrac{X-510}{85}>\dfrac{600-510}{85}\right)=\mathbb P(Z>1.059)\approx0.145$

So approximately 14.5% of the scores are higher than 600. This means in a sample of 7500, one could expect to see $0.145\times7500\approx10.86$ scores above 600.