The Normal
Distribution
The Normal distribution is a well-known shape, sometimes
referred to as the "bell curve" for its obvious similarity to a bell. In some
texts, it will be referred to as the Gaussian distribution after the
19th century mathematician Carl Friedrich Gauss. [11] The Normal distribution is very
important generally in the study of probability and statistics and useful to the
project manager for its rather accurate portrayal of many natural events and for
its relationship to something called the "Central Limit Theorem," which we will
address shortly.
Let's return to the coin toss experiment. The values of H and T are uniformly distributed: H or T can each
be either value 1 or value 0 with equal probability = 0.5. But consider this:
the count of the number of times T comes up heads in 100 tosses is itself a random
variable. Let CT stand for this random
variable. CT has a distribution, as do
all random variables. CT's distribution
is Normal, with the value of 50 counts of T at the center. At the tails of the Normal distribution
are the counts of T that are not likely
to occur if the coin is fair.
Theoretically, the Normal distribution's tails come
asymptotically close to the horizontal axis but never touch it. Thus the
integration of the PDF must extend to "infinite" values along the horizontal
axis in order to fully define the area under the curve that equals 1. As a
practical matter, project managers and engineers get along with a good deal less
than infinity along the horizontal axis. For most applications, the horizontal
axis that defines about 99% of the area does very nicely. In the "Six Sigma"
method, as we will discuss, a good deal more of the horizontal axis is used, but
still not infinity.
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