Binomial Distribution Calculator

Calculates the binomial distribution or the inverse binomial distribution.

The binomial distribution calculator computes the cumulative distribution (p) or the percentile (𝑥₁), inverse binomial distribution calculator

Choose 𝑥1 to calculate the cumulative t probability based on the binomial percentile, p(X ≤ 𝑥1) to calculate the t percentile based on the binomial cumulative probability, 𝑥1, 𝑥2 to calculate p(𝑥1 ≤ X ≤ 𝑥2) or p(X ≤ 𝑥1), p(X ≤ 𝑥2) to calculate x1, x2, p(𝑥1 ≤ X ≤ 𝑥2)

What is the binomial distribution?

The binomial distribution is a discrete distribution, that calculates the probability to get a specific number of successes in an experiment with n trials and p (probability of success).

When calculating the percentile, there is usually no X that meets the exact probability you enter. The tool will calculate the X that will generate a probability that is equal to or bigger than the input probability but will calculate the probabilities for both X and X-1.

When the tool can't calculate the distribution or the density using the binomial distribution, due to large sample size and/or a large number of successes, it will use the normal approximation with μ = np and σ=√(np(1-p)), or for the percentile calculation, it may be a combination between the two distributions using the binomial distribution whenever is possible.

What is the binomial distribution formula?

P(X=𝑥) = (𝑥)p𝑥qn-𝑥

What is the normal approximation for the binomial distribution?

Z =𝑥 - np
√(np(1 - p))