Random sampling simulation over samples (0 to 5000 samples)
We take a made up population and run a random sampling from 0 to 5000 samples and compare at each step the sample distribution with the population distribution.
We can see that at 1000 samples the sample fits quite well to the population.
Either way, 1 experiment proves nothing because it can be conditioned by the population of the distribution or by the specific sampling gotten. I repeated this several times and got similar results.