Hover over the chart to see the PDF - f(x) or PMF - P(X=x), as well as the Cumulative Distribution Function (CDF) - P(X ≤ x) and P(X > x).
Calculation steps
R Code
The following R code should produce the same results.
The Distribution Calculator and Inverse Distribution Calculator for Normal, Binomial, t, F, and other distributions compute cumulative probabilities (CDF), upper-tail probabilities (1 - CDF), probabilities between two values, probabilities outside two values, and probability density (PDF) or probability mass (PMF) functions.
Here is an example of a chart generated by the normal distribution calculator. The blue area represents the result for the “Calculate” option 'P(X ≤ 𝑥)' in this case:
The following distributions are supported:
Normal Distribution
Binomial Distribution
t Distribution
F Distribution
Chi Square Distribution
Poisson Distribution
Weibull Distribution
Exponential Distribution
Uniform Distribution
Select what you want to calculate:
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).
Z Score — the standard score, based on the mean and standard deviation. The Z distribution is normal with a mean of 0 and a standard deviation of 1. This option is relevant only to the Normal distribution.
Less/Greater or Less-equal/Greater-equal 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).
