Question

Some psychologists believe that a "genius" should be defined as anyone having an IQ over 140. If IQ scores are normally distributed with a mean of 100 and a standard deviation of 15, and if the population of the world is 6,575,000,000, how many geniuses are there in the world today?

A. 115,000
B. 24,985,000
C. 536,000,000
D. 123,000
E. 6,575,000

Answer 1

Let X be a random variable representing the IQ scores of people.
P(X > 140) = P(z > (140 - 100)/15) = P(z > 40/15) = P(z > 2.667) = 1 - P(z < 2.667) = 1 - 0.99617 = 0.00383

Therefore, the number of genuises are 0.00383 x 6,575,000,000 = 25,182,250

Option B is the correct answer