statistics help for Math 108

Question

The math scores for those taking the SAT test are normally distributed with a mean of 508 and a standard deviation of 120 (based on data from the College Board). Suppose a college includes a minimum math score of 650 among its requirements. What percentage of applicants score less than this, and therefore don't qualify for admission?

Answer 1

x = math score

want to find P(x < 650)

transform x from N(508,120) to N(0,1) by computing z score:

z score = (x - mean) / SD = (x - 508) / 120, where x = 650

P(x < 650) = P(x < (650-508)/120) = P(z < 1.18) = 0.881