Question

A social researcher has constructed a measure of racial prejudice and obtained a distribution of scores on this measure from a randomly selected sample of public office holders. the scores were normally distributed with a mean of 45 and a standard deviation of 7. what is the approximate probability that a randomly selected case from the sample will have a score less than 38?

Answer 1

To answer the problem mentioned above, below is the detailed solution:

z(38) = (38-45)/7]

-7/7 = -1

Z = -1

P(x < 38) = P(z < -1) = normalcdf

(-100,-1) = 0.1587

Therefore probability that a randomly selected case from the sample will have a score less than 38 is 0.1587