I need help with a math equation to describe a scenario. Here’s the scenario: Picture a large piece of cheese. There are 100 mice released at the same time that compete for the cheese. On average each mouse would get 1/100th of the cheese but if you looked at the distribution of mouse performance on a graph it would look like a bell curve with half the mice performing better than average and half performing worse. If we run this test a hundred times the average mouse will still get 1/100th of the cheese and the distribution of performance will still be a bell curve but the shape of the bell curve will change. If we assume that the performance of each mouse is random during each run (no inherent mouse skill) the bell curve should become more “narrow” but the center of the curve will remain in the same location. Eventually, if we run this to infinity the bell curve should in essence become a vertical line on the graph at 0.01 Any ideas how to describe this in an equation?

I need help with a math equation to describe a scenario.

 

Here’s the scenario:

 

Picture a large piece of cheese.  There are 100 mice released at the same time that compete for the cheese. 

 

On average each mouse would get 1/100th of the cheese but if you looked at the distribution of mouse performance on a graph it would look like a bell curve with half the mice performing better than average and half performing worse.

 

If we run this test a hundred times the average mouse will still get 1/100th of the cheese and the distribution of performance will still be a bell curve but the shape of the bell curve will change.  If we assume that the performance of each mouse is random during each run (no inherent mouse skill) the bell curve should become more “narrow” but the center of the curve will remain in the same location.  Eventually, if we run this to infinity the bell curve should in essence become a vertical line on the graph at 0.01

 

Any ideas how to describe this in an equation?