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.