Approximating the binomial distribution with a normal distribution

Approximating the binomial distribution with a normal distribution

Number of trials (n):

Probability of success (p):

Truncate x-axis

Instructions

The vertical bars show the Bernoulli distribution \(B(n, p)\), while the red curve represents the normal distribution with mean \(\mu = np\) and variance \(\sigma^2 = np(1-p)\). The normal distribution approximates the Bernoulli distribution well as long as \(np(1-p) \gg 5\). Use the sliders to adjust the number of trials \(n\) and the probability of success \(p\). When does the approximation break down?