The normal distribution has a greater percentage of its area close to the mean and much less in the tails.
-Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test). Find the IQ score separating the top 14% from the others.
A) 108.6
B) 99.3
C) 116.2
D) 83.7

Question

Quizplus · Accepted Answer

To find the IQ score separating the top 14%, we need to find the z-score that corresponds to the 86th percentile (100% - 14% = 86%). Using a standard normal distribution table or calculator, we find that the z-score corresponding to an 86th percentile is approximately 1.08.

Next, we use the formula for a z-score:

z = (x - μ) / σ

where x is the IQ score we want to find, μ is the mean IQ score of 100, and σ is the standard deviation of 15. Substituting in the values we know and solving for x:

1.08 = (x - 100) / 15

16.2 = x - 100

x = 116.2

Therefore, the IQ score separating the top 14% from the others is 116.2.

The Normal Distribution Has a Greater Percentage of Its Area