Normal Approximation to Binomial Distribution
- STATISTICS
Normal Approximation to Binomial Distribution Let $X$ be a binomially distributed random variable with number of trials $n$ and probability of success $p$.
The mean of $X$ is $\mu=E(X) = np$ and variance of $X$ is $\sigma^2=V(X)=np(1-p)$.
The general rule of thumb to use normal approximation to binomial distribution is that the sample size $n$ is sufficiently large if $np \geq 5$ and $n(1-p)\geq 5$.
For sufficiently large $n$, $X\sim N(\mu, \sigma^2)$.