# What are the chances of a sample distribution, given that I know the larger population's distribution?

I know that the larger population, of size m, follows a normal distribution. I have some sample that is size n, and follows its own particular distribution, which is not normal. Given my sample sizes, what are the chances that I would get the distribution that I did in my sample?

Additionally, if I know that the larger population does not follow a normal distribution, but I still know what its distribution is, is there a way to do this same calculation?

• The question is difficult to answer, since it is somewhat imprecise. A Kolmogorov-Smirnov test (see Wikipedia for a start) may be useful to you. More old-school traditional, particularly for the normal, are Chi-squared tests. – André Nicolas Aug 28 '14 at 16:05