Normal Distribution Calculator
The Distribution and Score calculators (inverse distribution calculator) compute cumulative probabilities (CDF), upper-tail probabilities (1 - CDF), probabilities between two values, probabilities outside two values, and probability density or mass (PDF/PMF) for many common statistical distributions:
For discrete distributions, use the "≤ / ≥" switch button to switch between "Less" and "Less-equal", and "Greater" and "Greater-equal".
For continuous distributions, we hide the button because p(X < 𝑥) is equal to p(X ≤ 𝑥).
- Normal Distribution
- Binomial Distribution
- T Distribution
- F Distribution
- Chi Square Distribution
- Poisson Distribution
- Weibull Distribution
- Exponential Distribution
- Uniform Distribution Calculator
- P(X ≤ 𝑥) — the cumulative probability based on the score.
- p(X ≥ 𝑥) — the upper-tail probability (1 − p) based on the score.
- P(𝑥₁ ≤ X ≤ 𝑥₂) — the probability that X lies between 𝑥₁ and 𝑥₂.
- P(X ≤ 𝑥₁), P(X ≥ 𝑥₂) — the probability that X lies outside the range 𝑥₁ to 𝑥₂.
- P(X = 𝑥) — for discrete distributions, the probability that X equals 𝑥 (PMF).
- PDF(X = 𝑥) — for continuous distributions, the value of the probability density function at 𝑥.
- Score 𝑥 from P(X ≤ 𝑥) — the score corresponding to a given cumulative probability p.
- Score 𝑥 from P(X ≥ 𝑥) — the score corresponding to a given upper-tail probability, 1 − p.
- Scores 𝑥₁, 𝑥₂ — the left score from P(X ≤ 𝑥₁) and the right score from P(X ≥ 𝑥₂).
For discrete distributions, use the "≤ / ≥" switch button to switch between "Less" and "Less-equal", and "Greater" and "Greater-equal".
For continuous distributions, we hide the button because p(X < 𝑥) is equal to p(X ≤ 𝑥).