[AntonioLao]

Two other names are (1) Gaussian distribution (2) error distribution. But why this distribution plays such a critical role in the theory of probability?

http://mathworld.wolfram.com/NormalDistribution.html

Is it because of its predictive power for making inferences about truly random events? Or is it because statisticians have no other options in their bags of tricks?

Is there such a thing as an abnormal distribution? Or its absence that makes the normal distribution so popular among insurance companies, market researches, public policies, IQ tests, opinion polls, medical treatments, economic analyses, biological growth studies, and one more but not last, psychoanalyses.

What does it really mean to be normal? Like average intelligence, average height, average weight, average income, middle ages, just surviving, no comment?

Why does humanity worship a law of averages? Can there be an average religious belief? This is a religion, which takes a condoning middle ground between good actions and bad actions, between constructivism and destructivism, between birth and death. A religion that only makes sense for the living.

One of the philosophical implications is that to be normal is to be alive, for it is in our desire to live that makes us seek the states of normality and nothing else.