Question

Scores on a certain standardized test have a mean of 500, and a standard deviation of 100. How common is a score between 600 and 700? Calculate the probability.

Answer 1

$\mu=500 \\ \sigma= 100 \\ P(600<X<700) = P(X<700) -P(X<600) \\ = P(Z< \frac{700-500}{100}) -P(Z< \frac{600-500}{100}) \\ = P(Z< 2) -P(Z< 1) \\ = 0.9772 -0.8413 \\ = 0.1359$