In the first place, I don't know what a "promblem" is. Is that where two boys ask the same girl to a formal high school dance? Or is it a bad computer chip?
In the second place, all postings are anonymous, so I have no idea what questions the phrase "...the above two promblems[sic]..." refers to.
The Central Limit Theorem says that if you have enough data, and you compute the mean or the variance of the data enough times, the mean and the variance will be normally distributed, more formally stated from Wikipedia:
"The central limit theorem (CLT) states that, given certain conditions, the arithmetic mean of a sufficiently large number of iterates of independent random variables, each with a well-defined expected value and well-defined variance, will be approximately normally distributed, regardless of the underlying distribution. To illustrate what this means, suppose that a sample is obtained containing a large number of observations, each observation being randomly generated in a way that does not depend on the values of the other observations, and that the arithmetic average of the observed values is computed. If this procedure is performed many times, the central limit theorem says that the computed values of the average will be distributed according to the normal distribution."
John
My calculator said it, I believe it, that settles it