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

Answer 1

Answer: Hello mate!

if 100 is the mean and 13 is the standard deviation:

(140 - 100)/13 ≈ 3

this means that the value where the geniuses start to appear is equal to the mean plus 3 times the standard deviation.

We know that the percentage that lies after the mean plus 3 times the standard deviation is 0.1% of the population.

Then, if the population is 6,575,000,000

the 1% of this number is equal to:

(1%/100%)*6,575,000,000 = 0.01*6,575,000,000 = 65,750,000

So there are almost 65,750,000 geniuses in the world.