Makes sense. I mixed up n and n-1

Probability function: X = (x1 + x2 + ... + xn)/n, where xi = xavg +/- dx

Xavg = xavg*n/n = xavg

dXavg^2 = n*dx^2/n^2
=> dXavg = dx/sqrt(n)

Xavg +/- dXavg = xavg +/- dx/sqrt(n)