I enjoy playing freecell online and have compiled some data from a week of play. I tend to do ok and started thinking about my abilities. Here are the numbers, but I don't know what methods would apply to this situation. Could someone help me out here.
I'm a beginning statistics teacher and thought I could reason this one out, but i'm lost.
Thanks for any help.

Given that after 72 contests, a contestant’s average finish is in the top two percent of all contestants entered in each event[Mean is actually .o179 computed as place divided by total contestants], with the standard of deviation of the finishes being 1.25%, what is the probability that the contestant is actually the best of all contestants?

The population of each contest varies from 800 to 23,000 participants. Many of them participate in the same contests.

How would one go about figuring this out?
Would a normal distribution analysis even apply here? I ran a normal distribution and with that mu and sigma it is a possibility.
One of the problems is this: A main assumption is that those finishing better then the contestant are most likely not the same individuals every time.How does one account for that, and does it matter: