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Notes on Topic 6:
Probability & Distributions

Probability and the Binomial Distributions

    1. 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.

    2. 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=1-P is the probability of the other event).

      Some examples of specific binomial distributions are given here.

    3. 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: