I would like to ask about the computational complexity of the problem of generating integers so that the obtained distribution is asymptotic to the Gaussian distribution. Any related reference is very appreciated.

More precisely, consider the following problem $\mathcal{P}$: generate $n$ integers between $-N$ and $N$ so that after scaling the interval to $[-1,1]$, one gets a distribution statistically close to Gaussian distribution, as $n, N$ tend to infinity. Is $\mathcal{P}$ NP-hard?