There is no reason to assume that types aren't evenly distributed. Maybe they are, maybe they aren't. MBTI test results are useless because they're two different systems and the people might be mistyped under that system anyway.

I have one word for Phaedrus. RANDOM. Sometimes things are random, or have an element of randomness in them. Types could be completely random, or partially genetic and partially random, or have some other partial biological cause and be partially random, etc. I'd believe they were 100% random before I'd believe that Asians are generally some given type.