The mean of normally distributed test scores is 77 and the standard deviation is 3. If there are 172 test scores in the data sample, how many of them were in the 68 to 71 range?

Question

answer options: 58, 4, 23, 82

Answer 1

First find the probability that a test score is in the 68 to 71 range.

Let x = test score. x is normally distributed with mean 77 and SD = 3

z = (x - mean)/SD is normally distributed with mean 1 and SD = 0

z = (x - 77)/3

P(68 < x < 71) = P( 68- 77/3 < z < 71 - 77/3) = P(-3 < z < -2) = P(z < -2) - P(z < -3) = 0.0228 - 0.0013 = 0.0215

Find how many of 172 in that range = 172 * 0.0215 = 3.698 ~ 4.