Estimating the IQ of Bill Gates

1590 on the SAT and the 5th richest man in the world

Given this information, a 1590 on the SAT would translate to roughly the same percentile as a perfect score - I’ll conservatively estimate he’s a 10 / 900000, which is a z-score of 4.24.

His wealth corresponds to a z-score of 6.

Assuming 0.84 correlation between SAT and IQ / 0.35 correlation between SAT and wealth, this is a pretty easy simulation

His cofounder Paul Allen who got a perfect score on the SAT has a z-score of 4.4 (5/924000), which translates to an estimate of 157.

SE is about 9.4 for both, derived from the SE that is generated from assuming that an individual scored above 155. A little unsophisticated, but better than nothing.

########################
set.seed(3)
g <- rnorm(60000000)
set.seed(4)
e <- 0.8*g + rnorm(60000000)*sqrt(1-0.8^2)

subby1 <- data.frame(g, e)
subby2 <- subset(subby1, (subby1$e > 3.66))
mean(subby2$g)*15
sd(subby2$g)*15