I'm wondering if anyone knows the answer to this:

For a set of X numbers with a median of Y and a standard deviation of Z, where a set determined randomly according to a Gaussian distribution would have a median of 0, what is the probability that the median Y indicates that the set of numbers is non-random? In other words, based on knowing how many numbers are in the set, what the median is, and what the standard deviation is, can one know the percent chance that the distance of the median from 0 reflects a non-random distribution of the set, versus the percent chance that the set could have been generated randomly? What would be the formula to determine this probability?

I'm asking because of an interest in analyzing financial data to determine non-random patterns.

Thanks.