Question

IQ scores form a normal distribution with μ = 100 and σ = 15. Individuals with IQs between 90 and 110 are classified as average. What proportion of the population is average?a. 0.7486

b. 0.5028
c. 0.4972
d. 0.2486

Answer 1

The proportion of the population that has an IQ between 90 and 110 and is classified as average is a. 0.7486

How to find the proportion ?

Convert the IQ scores to standard scores (z-scores) using the formula:

z = (x - μ) / σ

An IQ score of 90 would have a z-score of:

z = (90 - 100) / 15

= -0.67

An IQ score of 110 would have a z-score of:

z = (110 - 100) / 15

= 0.67

Using a z-score table, you would find the area corresponding to 0.67 (one-tailed) and subtract it from 1 (total area under the curve). This gives you:

Proportion of average IQ = 1 - area(0.67)

= 0.7486

In conclusion, 74.86% of the population has an IQ between 90 and 110 and is classified as average.