For an assignment I've been asked to investigate the CLT when sampling from different distributions using different sample sizes. Do to this in R, I've created histograms of the binomial, poisson, and uniform distribution each with 10, 100, 1000 samples of sample sizes of 10, 20, 50,and 100 (with a long-winded code that am also going to try to fix up at a later data).

As I understand, as sample size increases, the distribution of means approximates a normal distribution. I can see this clearly in my histograms when I increase the number of samples (or the number of replicates of 10, 20, 50, and 100 that I take), but not when I increase the sample sizes. Increasing the sample sizes from 10 to 50, for example, does not seem to bring in the tails of the distribution or approximate the normal distribution any further. My guess was that increasing both sample size and replicates helped increase the tendency towards meeting the CLT. Am I missing something?

Thanks,

lken