Scores of adults on the Wechsler Adult Intelligence Scale (a common IQ test) follow a Normal distribution. The middle 95% of scores on this test range from 70 to 130. What is the standard deviation of the test scores?
A) 100 points
B) 20 points
C) 15 points
D) 7.5 points
E) 5 points

Question

Quizplus · Accepted Answer

Since the middle 95% of scores range from 70 to 130, this means that the remaining 5% of scores are outside of this range, with 2.5% of scores below 70 and 2.5% of scores above 130. Since the Normal distribution is symmetrical, we can find the z-scores corresponding to the 2.5% tails on either side of the mean by using a standard Normal distribution table or calculator. The z-score that corresponds to the 2.5% tail on either side is approximately 1.96.

Now we can use the formula:

z = (x - μ) / σ

We know that when z = 1.96, x = 130 and when z = -1.96, x = 70. We also know that the mean μ is halfway between these values, so:

μ = (130 + 70) / 2 = 100

Substituting all of these values into the formula, we can solve for the standard deviation σ:

1.96 = (130 - 100) / σ 
σ = 15.15

Therefore, the standard deviation of the test scores is approximately 15 points. Choice C is the correct answer.

Scores of Adults on the Wechsler Adult Intelligence Scale (A