I would be happy to take a bet that took a random sample of people that we knew (let’s say 10) and saw whether their responses fit more with a log-normal or a normal distribution, though I do guess this would be quite indiscriminate, since we are looking for divergence in the tails.
Quick sanity check:
4.5SD = roughly 1 in 300,000 (according to wikipedia)
UK population = roughly 50 million
So there’d be 50 * 3 = 150 people in the UK who should be able to get scores at ~21 or more. Which seems quite plausible to me.
Also I know a few IMO people, I bet we could test this.
I would be happy to take a bet that took a random sample of people that we knew (let’s say 10) and saw whether their responses fit more with a log-normal or a normal distribution, though I do guess this would be quite indiscriminate, since we are looking for divergence in the tails.