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Probability Calculator

Probabilities for normal, binomial and Poisson distributions.

Details

Results

P(exact)
P(≤)
P(≥)
P(>)

Computed with standard statistical methods in your browser.

How it works

Normal uses the cumulative normal curve; binomial uses the exact mass function with log-factorials for stability; Poisson uses e^−λ λ^k ÷ k!. We report exact and cumulative probabilities.

Choosing a distribution: normal for continuous data, binomial for fixed trials with two outcomes, Poisson for counts over an interval.

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Good to know

FAQs

When do I use the normal distribution?

For continuous, roughly bell-shaped data described by a mean and standard deviation.

What is the binomial distribution?

The probability of k successes in n independent trials each with success probability p.

When is Poisson appropriate?

For counts of rare events over a fixed interval, defined by an average rate λ.

What does P(≤) mean?

The cumulative probability of getting that value or fewer.

Are large n binomials accurate?

Yes — we use log-factorials to stay accurate for large n.