Also, I don't think what you're saying about the Gaussian distribution is true for GRE Subject tests as they have significantly varying distributions. Check out this table:
I had a 'qualification': "Usually the CEEB, SAT, and GRE", and with that we both can be right!
For those tests, at the level of detail of the distribution of the scores, it can be tough to get solid data.
But it is easy and common in educational testing to scale 'raw' scores so that the 'scaled scores' are Gaussian.
Also in educational testing, it is easy and common to have enough data on individual questions so that the distribution will be known fairly accurately for a test made of such questions -- my father did that for years as the main 'educational architect' at one of the world's largest and most important technical schools, with 40,000 students there at any one time.
Having those tests be accurately Gaussian more than
2.5 standard deviations away from the mean is likely challenging. I've often suspected that on some of the SAT tests they didn't give any 800 scores.
There have been suggestions that those testing companies have not always been very open about just what they were doing in their details!
http://www.ets.org/s/gre/pdf/gre_guide_table2.pdf
It would appear that GRE Physics is the easiest test, while Biochemistry is the hardest.