How Normal is the Normal Distribution

A young man in Naval Uniform sat at a table with beads of sweat forming around his short cropped hair. His left wrist was bound with the index finger laid flat on the wooden surface. Above his finger rested the chef’s cleaver with the front point pointed downward, piercing the wax film of the table. The rear of the sharp blade ready to dissect with the slightest push by the firm worn hand of his captor.

“The rules are simple,” spoke the older man holding the cleaver. “Strike your lighter ten times,” he gleefully explained with grip tightening, “If any of the ten strikes fail, I take the finger.” “But I get the car if each strike works,” the Sailor interjected with a hint of trepidation. “Yes, yes” assured the man holding the knife with slight annoyance.

The Navy man’s right hand held a metallic lighter with his finger on the wheel. “One,” spoke the captor. With slight pause the seaman flipped the wheel of the lighter. A spark and flame appeared. “Two,” came the voice with increased anticipation. The lighter flicked again with spark and flame. “Three,” burst the man with a gleeful shout.

Like much of probability, the foundations for the Normal Distribution comes from gambling. In 1733, Abraham de Moivre discovered that the random act of flipping a coin (Binomial Distribution) approached a very smooth curve as the number of iterations increased. Since that time, it was found that the Normal Distribution appears in many natural phenomenon. Making it a basis for Statistical Inference.

It seems that most, if not all, measures dealing with humans fit the Normal Distribution or Bell Curve as it is commonly called. Everything from employee salaries, Intelligence Quotient (IQ), Grade Point Average (GPA), likelihood for chronic illness, and more fit into this model. At first, one may assume this is due to such measures being contrived to fit a simple model like the assumption in High School Physics that gravity is constant. However, looking deeper into the subject brings up some interesting discoveries.

With the sailor’s right thumb indented onto the wheel, a strike occurs and flame appears. “Four,”…

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