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.