Elon Musk’s SAT score is reasonably high at a 1400 - about 3 (not 2.59 as I had originally calculated, this was a mistake) SD above the mean. Beyond that, he also scored extremely highly on a computing test - no norms are published so I will simply assume he scored at a 1/200 or above. This is a little rough and dirty, but an estimate of ability for somebody who coded their own game at 12 years old seems reasonable. The testers specifically said that they had never seen somebody score that high on the test, and I would assume that somewhere between 100-10000 people got tested, though it’s difficult to make an exact inference. “Never having seen somebody score that high” could also simply be an exaggeration as well, so there is some uncertainty in this report.
It’s very difficult to simulate the IQ of somebody who is so wealthy, so I had to settle for individuals who were above 4 standard deviations in wealth, which is similar enough, but will lead to an underestimation of roughly 1-2 points.
Assuming a correlation between SAT and IQ of .84, a correlation of wealth/income with IQ of .35, and a correlation between technical ability and IQ of .6 yields the following estimate:
mean: 148
standard error: 7.6
n: 156
v <- c()
for(i in 1:100) {
set.seed(i)
g <- rnorm(60000000, mean=0)
iq <- 0.84*g + rnorm(60000000)*sqrt(1-0.84^2)
sc <- 0.35*g + rnorm(60000000)*sqrt(1-.35^2)
tk <- 0.6*g + rnorm(60000000)*sqrt(1-.6^2)
subby1 <- data.frame(iq, sc)
subby1$g = g
subby1$ed = ed
subby1$sc = sc
subby1$tk = tk
subby2 <- subset(subby1, (subby1$iq > 2.7) & (subby1$iq < 3.3) & (subby1$sc > 4) & (subby1$tk > 2.57))
v <- c(v, subby2$g)
}
qnorm(1/200)
mean(v)*15
sd(v)*15