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 17 and if the population of the world is
6,575,000,000, how many geniuses are there in the world today?

Answer 1

61.8 million

Explanation:

Find the z-score of 140:

z = (x − μ) / σ

z = (140 − 100) / 17

z = 2.35

Use a calculator or z-score table to find the probability:

P(z > 2.35) = 1 − 0.9906 = 0.0094

0.94% of the population is above 2.35 standard deviations. If the size of the population is 6575 million, then 0.94% of that is:

0.0094 × 6575 million ≈ 61.8 million