SAT verbal scores are normally distributed with a mean of 410 and a standard deviation of 93. Determine what percent of the scores lie between 503 and 689.

Answer 1

x is SAT score x is N(410,93)

want to find P(503 < x < 689)

transform to N(0,1) using

z = (x - mean)/SD = (x - 410)/93

compute z for x = 503 (call it zlower)

compute z for x = 689 (call it zupper)

then P(503 < x < 689) = P(zlower < z < zupper) = P(zupper) - P(zlower)

find probabilities from standard normal probability distribution lookup