The Central Limit Theorem

Here's a question to ponder:  Suppose that you sampled from a distribution other than the normal (bimodal, skewed, or uniform distribution). Would the means () of the samples conform to the shape of the distribution from which they were attained if were to present them graphically?

An important concept to understand is the Central Limit Theorem, which states that the sampling distribution of the sample means of a population tends to be a normal distribution if the sample size is acceptably large enough.  This is true regardless of the shape of the Population's distribution.

We know intuituvely that the larger the sample size n , the closer we come to the true population mean and variance.  Additionally, given multiple samples with mean = , the sample mean would closely approximate the true Mean.  But what is the exact relationship between the sample size n  and the mean and standard deviation?