Binomial Distribution
Analysis Of Statistical Data

Binomial Distribution
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Binomial Distribution

A special case of the poisson distribution

The binomial distribution (BD) is one of the most important distributions in statistics. This distribution is the discrete probability distribution (the variable can take only fixed values) of the number of successes in n independent trials, each with the same probability of success or failure.

Suppose a coin is tossed ten times. The probability of the coin showing heads or tails is ½ (p=0.5; both are equally likely). The BD for this success /failure experiment (also known as a Bernoulli trial), expressed as b (10,5) is the probability distribution of how many times the coin will show heads.

Processes That Exhibit A Binomial Distribution

BDs are characteristic outcomes of the processes in which following conditions are met:

Statistics of Binomial Distribution

Example of Using the Binomial Distribution:

Binomial Distributions

Normal Approximation of
the Binomial Distribution

If the number of trials is large (n>20) and the probability of success and failure are almost equal, then the binomial distribution can be approximated by the normal distribution. This approximation is useful to find an unknown probability of success/failure by using a fairly large number of trials (for example, asking 100 people if they like a particular brand of shampoo etc).


The binomial distribution is a discrete probability distribution which describes the probability of success (or failure) of a Bernoulli experiment. A Bernoulli experiment consists of n repeated trials of the same type, each with the same probability of success (p) or failure (1-p),

and a trial can only have two outcomes (YES/NO, success/failure etc). The distribution can be approximated by the normal distribution, if a large sample is used (n>20).

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