When is to use binomial distribution

This article is a continuation from the previous Binomial distribution article. It may be a good idea to go through that article before attempting this article. This article explores the conditions when a binomial distribution is a suitable model.

In the previous article example there were 4 conditions explored for binomial distribution. We shall list the conditions here;

• A fixed number of trails, n

  A binomial distribution is suitable when there is a fixed number of trials. In the above example the coin was thrown 10 times. So n=10 was fixed.

• Each trail should be success or failure

  The distribution is called binomial because there are only 2 cases for each trial. In the above example each throw could land on heads (H) or tails (T)

• The trials are independent

  The trials must be independent i.e you must be able to multiply the probabilities together.

• The probability of success, p at each trail must be constant

  In the above example we assumed that the probability was p at each throw.

If the above conditions are satisfied we say that the random variable X ( = the number of success in n trials) has a binomial distribution which can be written as;
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…where…

• ’B’ for binomial
• n for the number of trials
• p for the probability of success at each trial

…then…
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n is often referred to as the index and the parameter of the binomial distribution.
Below we shall look at some examples using the equation above.