Suppose that, by 2050, geneticists have identified the several hundred genes responsible for cognitive ability. Moreover, they have conducted extensive sampling on two geographically isolated human populations. When analyzing the distribution of cognitive ability, they found that the following: In population A, cognitive ability was normally distributed with a mean of 110 and a standard deviation of 10. In population B, cognitive ability was normally distributed with a mean of 110 and a standard deviation of 12.25, i.e., 25% greater than in population A.

a. What value of cognitive ability represents the 99% quantile for (show work)

i. population A?

ii. population B?

b. What fraction of population B lies above the 99% quantile of population A? Show work.

c. If all else is equal (in terms of environmental conditions, economic opportunity, etc.), which population is more likely to yield the next Einstein (let's define "the next Einstein" as someone with cognitive ability exceeding 180)? How much more likely? Support your answer.