Some IQ tests are standardized to a Normal model with a mean of 100 and a standard deviation of 16. About what percent of people should have IQ scores above 116?
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion above that Z score.
To find the percentage of people who should have IQ scores above 116, we first need to convert the IQ scores to z-scores using the formula:
z = (X - μ) / σ
Where:
X = IQ score
μ = mean (100 in this case)
σ = standard deviation (16 in this case)
Plugging in the values into the formula, we get:
z = (116 - 100) / 16
z = 16 / 16
z = 1
Now, we need to find the area under the standard normal distribution curve that corresponds to z = 1. We can look up this value in a standard normal distribution table or use a calculator.
From the standard normal distribution table, the area to the left of z = 1 is approximately 0.8413. Since we want the area to the right of z = 1 (above 116), we subtract this value from 1:
1 - 0.8413 = 0.1587
So, approximately 15.87% of people should have IQ scores above 116.