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 probability that a randomly selected case from the sample will have a score less than 38?
A) 0.4526
B) 0.5018
C) 0.5200
D) 0.1587

Question

Quizplus · Accepted Answer

To calculate the probability that a randomly selected case from the sample will have a score less than 38, we need to find the area under the normal distribution curve to the left of 38. We can standardize the score using the formula:

z = (x - μ) / σ

where x is the score we want to calculate the probability for, μ is the mean of the distribution, and σ is the standard deviation of the distribution. Plugging in the values, we get:

z = (38 - 45) / 7 = -1

We look up the probability corresponding to z = -1 in the standard normal distribution table or use a calculator to find that the area to the left of z = -1 is 0.1587. Therefore, the probability that a randomly selected case from the sample will have a score less than 38 is 0.1587 or approximately 0.16. The correct choice is D.

A Social Researcher Has Constructed a Measure of Racial Prejudice