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

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Answer 2

\[Z=\frac{140-100}{17}\approx2.35\]\[\Phi(2.35)=0.9906\]So the proportion of people that would be classed as genius is: \[1-0.9906=0.0094\]So the amount of genuises is:\[0.0094\times6.575\times10^9=61,805,000\]