If the resistor values are distributed as a Gaussian where the tolerance is some confidence interval, then the total resistance of resisters in series would be

If the resistor values are distributed as a Gaussian where the tolerance is some confidence interval, then the total resistance of resisters in series would be distributed as the sum of those Gaussians whose tolerance would be the root-sum-square of the individual tolerances: sqrt(tol1^2 + tol2^2 + ... tolN^2), or if all the tolerances are the same then sqrt(N)*tol.