Luck Run Amok—Part 8

Explaining a Paradox

In my last post, I noted this seeming paradox:

If IQ scores and other measures of abilities within a profession are approximately normally distributed, why aren’t income and wealth within that profession normally distributed, too?

My first attempt at an explanation was based on the fact that the tails of the normal distribution are very skewed. Figure 1 shows a hypothetical normal distribution for one type of ability with the average score equal to 100 and the extremes scores capped at 50 and 150.

Figure 1 Normally Distributed Abilities

Those in the middle 10% of the distribution are pretty much indistinguishable, with abilities ranging from 98 to 102. On the other hand, the 90th percentile is at 119 and the 99.9th percentile is at 146. It makes sense, then, that income would be skewed, with a person at the 99th percentile paid much more than someone at the 90th percentile and someone at the 99.9 percentile paid even more.