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Chapter 9: The Normal Probability Distribution
Figure 9-4:
The normal probability distribution approximation
as the limiting distribution for the binomial distribution
when
p
= 0.85
Based on the observations from
Figures 9-2
to
9-4
, we can generally say
that as the sample size increases, the distribution for the binomial random
variable will converge to the normal distribution. The rate of convergence
will depend on the probability
of success for the binomial random variable
in the binomial experiment.
As previously mentioned, the normal distribution may be considered the
most important probability distribution in all of statistics. It is used to
describe the distribution of many natural phenomena, such as the height of a
person, IQ score, weight, blood pressure, observational error in an
experiment etc.