I expect people to have a better idea of group sizes than normal distributions, but the worry is with 'chosen uniformly at random,' since people tend to be in IQ bubbles. If you can think of 100 people you know dumber than you, and 10 people you know smarter than you, then you might say "well, that implies a group size of about 10," without realizing that half of those people you know from graduate school where the average IQ is in the top percentile.

But it seems like we can compare that to SAT scores and measured IQ (if provided) and that'll give us useful information.

I've also edited it so it's a little less ambiguous (were you randomly selected before or not?) but I want to add the super formal mathematical version to make it totally unambiguous, which may or may not be a good idea.