Considering X to be the sum of random variables of samples of the population (X1 + X2 + … + Xn), with mean n*mu and std `(sqrt(n)*sigma)`

.

The transformed variable `Y = (X - mu)/sigma`

converges to a normal distribution with mean 0 and std (sqrt(n)) instead of 1 as is being suggested. I tried the problem both empirically as well as from mathematical theorems.

Please clarify.

Thank You