Written by the Fiveable Content Team • Last updated August 2025
Written by the Fiveable Content Team • Last updated August 2025
Definition
Normal approximation to the binomial is a method used to approximate the probabilities of a binomial distribution using the normal distribution when the sample size is large and the probability of success is neither very close to 0 nor 1.
The normal approximation can be applied when both $np \geq 10$ and $n(1-p) \geq 10$, where $n$ is the number of trials and $p$ is the probability of success.
To use the normal approximation, continuity correction is applied by adjusting the discrete binomial variable by ±0.5.
The mean ($\mu$) of the approximating normal distribution is given by $np$, and its standard deviation ($\sigma$) is given by $\sqrt{np(1-p)}$.
This approximation simplifies complex binomial probability calculations, making them more feasible for large samples.
Normal approximation becomes more accurate as the sample size increases.
A theorem that states that, given a sufficiently large sample size from a population with a finite level of variance, the sample means will be approximately normally distributed.
A discrete probability distribution that describes the number of successes in a fixed number of independent Bernoulli trials with constant probability of success.