Probability
and the Binomial Distributions


 Definition
 When a variable is measured on a scale consisting
of only two categories, the data are called
binary or binomial. In this situation the researcher
often knows the population probabilities associated
with the two categories. When this is the case,
the data have a known population distribution, called
the binomial distribution.

 Distribution Shape
 There are a whole family of different binomial
population distributions. The exact shape of a member
of the family depends on:
 N, which is the number of observations
or individuals in a sample.
 P, which is the probability of one
of the two events (Q=1P is the probability
of the other event).
Some examples of specific binomial distributions
are given here.

 Normality of Binomials
 When the product of N and P and the product of
N and Q are both greater than or equal to 10, the
binomial distribution is nearly perfectly normal.
Under these circumstances:
 The population mean is NP
 The population standard deviation is SQRT(NPQ)
Demonstration of Normality of Binomial:

