A-level Mathematics/MEI/S1/The Binomial Distribution

Conditions for a situation to be normally distributed

If a situation is to be binomially distributed it must satisfy the following conditions.

1. The event must have only two possible outcomes.The outcomes are normally termed as 'success' ( denoted by $$p$$ ) and failure ( denoted by $$q$$ )

2. The two outcomes must be independent.

Converting Binomial distribution into a Normal Distribution
If an event is to be repeated $$n$$ number of times with constant (independent) probabilities of both the possible outcomes occurring, by calculating the mean ($$ n * p$$ ) of the distribution and the variance ( $$n * p * q$$ ) of the distribution, the binomial distribution can be converted into an approximate normal distribution.