Probabilities

"What are the chances, eh?" asked the cop. "... that I'd pull you over twice in one week?"
Considering the fact that as I waited 10 minutes for him to run up the ticket, I watched well over 100 cars go through the stop sign without stopping, and that I had not gotten a ticket in many years - I'd say the probability is pretty low.

At a party this weekend, someone brought up mbti (personality type) and I reacted with determination to piss all over it. I explained a central fallacy with the idea that traits are normally distributed, so the probability of being a particular "true" type are vanishingly slim. I've written about this before, but I feel like makeing a correction and adding a little explanation. (And what is the probability that someone will actually read both entries?)

In a normal distribution, 68% of the values will be within one standard deviation of the mean. In regards to personality type, 68% of people are normal for a trait and only (100% - 68% =) 32% are "outside of the norm". For two traits, only (32% x 32% =) 10% of people are "outside of the norm" for both traits. For three traits, only 3%; and for four traits, only 1%.
So, only 1% of the population is actually a "true type", (e.g. intp, esfj).

Traits Probability
0 68%
1 32%
2 10%
3 3%
4 1%