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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?

A115,000
B24,985,000
C536,000,000
D123,000
E6,575,000

Verified Answer :

nobillionaireNobley

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

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