Binomial Distribution Calculator
Calculate P(X=k) = C(n,k) * p^k * (1-p)^(n-k).
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Enter the number of trials (n), the number of successes (k), and the probability of success on each trial (p). The calculator computes the exact binomial probability P(X=k), along with cumulative probabilities and distribution statistics.
About This Calculator
The binomial distribution models the number of successes in a fixed number of independent trials, each with the same probability of success. It is used in quality control, polling, medical trials, and any scenario with repeated yes/no experiments. The formula is P(X=k) = C(n,k) * p^k * (1-p)^(n-k).
Frequently Asked Questions
When should I use the binomial distribution?
Use it when you have a fixed number of independent trials, each with the same probability of success, and you want to know the probability of a specific number of successes.
What is the mean of a binomial distribution?
The mean is n * p, and the standard deviation is sqrt(n * p * (1-p)).
When does the binomial approximate the normal?
When n is large and p is not close to 0 or 1 (commonly when np > 5 and n(1-p) > 5), the binomial distribution is well approximated by the normal distribution.