Willie Sutton and the multivariate normal distribution

https://www.johndcook.com/blog/2011/09/01/multivariate-normal-shell/

a multivariate normal in d dimensions with d large has roughly 95% of its probability mass in a shell of radius √d with thickness 4, two standard deviations either side of √d. (I'm approximating anyway, so I approximated √(d-1) as √d to make the conclusion a little simpler.)

_- Steve