Greetings,
IMJohnCox
As a life-long d-pawn player, I'm enjoying both of your recent d-pawn books! Thank you for writing them!
Smyslov-Fan Thank you for the - on the whole - positive "review" of my post.
However, I may have caused some minor confusion in my use of the term "professional".
I didn't mean it in terms of "earning a living" but rather in how regularly a person plays. Granted, those playing regularly in graded tournaments will, most likely, be earning some form of living from doing so.
However, I was thinking more in terms of those who are assiduously improving their ratings on the way to becoming World Champion. The "serious" chess players!
The percentiles, as quoted, should have been accompanied with the appropriate titles.
When I posted that, it was 3am and I was too lazy (tired!) to be bothered checking the FIDE website for the appropriate titles/ratings.
Let me try afresh:
80% = 2240 (NM)
85% = 2380 (IM?)
90% = 2520 (FM?)
95% = 2660 (GM)
98% = 2744
Having checked the site, I'm not altogether certain how the FM and IM titles rank - which is "higher"?
My approach may have been somewhat naive - statistically, at least. I wasn't trying to recreate the population curve from the current highest rating.
My basic idea in the use of percentiles was to make it easier to work-out suitable thresholds for titles in a dynamically-changing environment.
(In time - how long, I'm not certain! - people will pass the 3000-mark and keep on going.

)
You'll note that the 95-percentile roughly matches the current GM threshold, although it moves it upward - which is what some have suggested.
More importantly, when I originally wrote the above, I had it in mind that the 98-percentile is the elite group in which you would find the current Champion and most likely Challenger(s).
(Not intended as a threshold for a new "title".)
As an aside, as you clearly are statistically-minded, perhaps you could cross-check all the previous World Champions' ratings at the time they were playing a Challenger - I think you'd find that they would both be within this percentile compared with the contemporary highest rating.
Kindest regards,
James