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Updated 2026-03-07 UTC
Binomial Distribution Calculator — PMF, CDF, and Inverse
Compute binomial probabilities (PMF/CDF) and quantiles with GetCalcMaster’s stats functions. Includes worked examples (educational).
The binomial distribution models the number of successes in n independent trials with success probability p. Use this guide for PMF (exact probability), CDF (cumulative probability), and inverse CDF (quantiles).
Important: This content and tool are for educational purposes only. Outputs are estimates; always cross‑verify with official sources and/or a qualified professional.
What this calculator is
The Statistics Calculator is an interactive tool inside GetCalcMaster. It’s designed to help you explore scenarios, understand formulas, and document assumptions.
Key features
- Immediate results as you change inputs
- Transparent assumptions and explainable outputs
- Works well with the built‑in Notebook for saving scenarios
Formula
PMF: P(X=k) = C(n,k) p^k (1−p)^(n−k)
CDF: P(X ≤ k)
Quantile: smallest k with CDF(k) ≥ qQuick examples
binompmf(7, 20, 0.4) # ≈ 0.165882binomcdf(7, 20, 0.4) # ≈ 0.415893binominv(0.95, 20, 0.4)# Sanity check: CDF should increase with k binomcdf(8, 20, 0.4) - binomcdf(7, 20, 0.4)
Verification tips
- CDF should be non-decreasing as k increases.
- PMF values should sum to ~1 over k=0..n (within rounding).
- Use consistent definitions for a ‘trial’ and ensure independence is reasonable.
Common mistakes
- Mixing up k and n (k is successes, n is total trials).
- Using p as a percent (40 instead of 0.40).
- Assuming independence when trials are dependent (can break the model).
How to use it (quick steps)
- Set n (number of trials) and p (success probability).
- Decide whether you need PMF, CDF, or inverse CDF.
- Open the Statistics Calculator and use binompmf(k, n, p), binomcdf(k, n, p), or binominv(q, n, p).
- Verify that probabilities are between 0 and 1, and that CDF is non-decreasing in k.
- Document the trial definition and the independence assumption.
Related tools and guides
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Pearson r interpretation cautions.
Math hub
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FAQ
What does binompmf(k,n,p) compute?
The probability of exactly k successes in n trials with success probability p.
What does binomcdf(k,n,p) compute?
The probability of at most k successes: P(X ≤ k).
What does binominv(q,n,p) return?
The smallest integer k such that P(X ≤ k) ≥ q.
Tip: For reproducible work, save your inputs and reasoning in Notebook.