Explaining why process obeys Central Limit Theorem I'm trying to explain why some complex process obeys Central Limit Theorem.
The process is a chip compiler that runs complex place & route algorithms. The input is an integer seed. It initializes the algorithms in a random way. The output is a real number, which determines quality of results; the higher the number - the better. Exact implementation of place & route algorithms is not known. But their goal is to reach quality of results be positive.
I run 100 compiles with different seeds. When I plot a histogram of the results, it looks like a normal distribution. I tried different designs, tool versions, etc., and always get nicely shaped normal distribution, but with different mean and variance.
I strongly suspect that Central Limit Theorem plays a role here. But why? 
Why would a complex place&route algorithm obey CLT, if it has nothing to do with any random distribution. Or maybe the interpretation of the results has nothing to do with the CLT.
Below is a process block diagram and example of the results.

 A: One important point that many seem to be confused about is the application of the Central Limit Theorem (CLT). The CLT applies to the arithmetic mean of a distribution—not the distribution itself. Given an increasing number of samples, the average of those samples tends to be normally distributed with the "mean mean" equal to the overall mean and the variance of that mean estimator proportional to the variance and the number of samples. The actual distribution itself is not going to be normal. If anything, the distribution of the samples (NOT their average) will flesh out the shape of the distribution and you will have a greater chance of seeing an extreme value the more samples are generated.
My hunch is that your routing score is probably an average of some values, and, as such, is the mean of some distribution. If so, as the mean of a distribution, under many conditions its own distribution will tend to the normal after enough samples are generated.
A: Although I don't know anything about circuit design, I'm confused as everyone else why you would expect results to cluster around the average. The CLT has to do not with the shape (as many have correctly pointed out) but the probability of each a data point landing into a random a subset. If the underlying process had a bi-modal distribution, most of the samples would have skinnier peaks.  
If your random seeds determine the efficiency of their placement and there is some sort of upper and lower bound on performance then your numbers simply reflect the distribution of such locations.
