hi,

my understanding if the CLT is that if you take samples fron your population, which may have any distribution whatsoever, the mean value if the sample will be approximatively normally distributed. So, in your example, if you take 10 stones, say, calculate the mean of the ten, then put the stones back and repeat - the mean value of the distribution of the calculated means will be 5.5 with a given std dev std=3/sqrt(120). If the distribution of the numbers in your population is not uniform but something else then the mean value of the sample means and the std dev of the sample means will change accordingly, but the distribution will stay normal.

AFAIK the CLT will not help you to figure out the underlying distribution, to do that you would need to run specific tests. What it might help you with is the other way of reading the CLT : if your data is generated by a process that is the sum if small independent random effects then you can expect that your data will be approximatively normally distributed.

regards