There is no proof that personality traits have any identifiable distribution, let alone normal distribution.

Heck we don’t even know what personalty is, or if it is even a useful scientific term. Evidence suggests that peoples behavior varies wildly between situations, way more then any preconceived notion of behavior dictated by personality.

If tests show a normal distribution of a personality trait, it is most likely because it has been standardized to do exactly that. Not because people’s behavioral patterns align neatly in our favorite distribution.

Good thing it's not a measure of behavior, but of preference.

If preference does not correlate with behavior, you are effectively measuring nothing.

However it does correlate with behavior, otherwise personality traits would be completely dead as a science. But the effect is very weak next to the effect of the situation. Diverse personality traits will cheat if the environment is conducive to cheating behavior.

I would put personality in the same camp as religious believes or political leanings. An effect that mildly alters behavior, but not enough to actually matter in most circumstances.

> If preference does not correlate with behavior, you are effectively measuring nothing.

Preference is not nothing. It reflects what people like and want.

Preference for these traits, e.g. introversion, is a fairly reliable predictor of behavior, but it doesn't matter if it is or not, if someone lies to themselves entirely (however likely that is). The purpose is regurgitating to the test-taker what they like and want. I don't see how a company could make good use of it.

So you would have trouble telling whether a given person is taller or shorter than average?

Thanks for illustrating what parent comment said: it would be ridiculous to categorise only between “tall” and “short” when most people would fall into “kinda average”

A friendly reminder that height is not normally distributed either. Within a population it has a bimodal distribution.

Also a friendly reminder that a quarter standard deviations above the mean vs. the same distance below the mean is quite often a trivial difference in population statistics. And it should be nonsense (pseudoscience if you will) to make the distinction. A much more interesting statistic are the outliers. And grouping an outlier with a person who is 0.05 SD from the mean is just confusing at best.

Does it have a bimodal distribution because you're combining male and female normal distributions?

Partially yes. But a distinguished homogeneous population of a single gender probably has a normal distribution. Luckily humans usually don’t live in a distinguished homogeneous population of a single gender, so comparing your self to the average is at best fun. (unless you are an outlier, then it can be interesting or medically useful).