IQ scores (as measured by the Stanford-Binet intelligence test) are normally distributed with a mean of 100 and a standard deviation of 16. Find the approximate number of people in the U.S. (assuming a total population of 280,000,000) with an IQ higher than 120.
Round your answer to the nearest 100,000.

A)30,600,000 people
B) 265,200,000 people
C) 29,600,000 people
D) 250,400,000 people
E) 132,600,000 people

Question

IQ scores (as measured by the Stanford-Binet intelligence test) are normally distributed with a mean of 100 and a standard deviation of 16. Find the approximate number of people in the U.S. (assuming a total population of 280,000,000) with an IQ higher than 120. ​
Round your answer to the nearest 100,000.
​
A)30,600,000 people
B) 265,200,000 people
C) 29,600,000 people
D) 250,400,000 people
E) 132,600,000 people

Quizplus · Accepted Answer

First, we need to find the z-score for an IQ of 120:

z = (120-100)/16 = 1.25

Using a standard normal distribution table, we find that the probability of getting a z-score of 1.25 or higher is 0.1056.

So, the approximate number of people in the U.S. with an IQ higher than 120 is:

0.1056 x 280,000,000 = 29,568,000

Rounding to the nearest 100,000 gives us a final answer of 29,600,000. So, the correct choice is C.

IQ Scores (As Measured by the Stanford-Binet Intelligence Test) Are