Continuity Correction Calculator
Compare normal approximation results for binomial probabilities, with or without the continuity correction.
Binomial mean (μ): 20.000
Standard deviation (σ): 3.162
P(15 ≤ X ≤ 25) without correction: 88.62%
With continuity correction: 91.80%
How to Use This Calculator
- Enter the number of binomial trials, success probability, and the inclusive range of successes.
- Review mean and standard deviation of the approximating normal distribution.
- Compare normal approximation probabilities with and without the continuity correction ±0.5.
- Use the corrected result for better accuracy, especially with smaller n or extreme probabilities.
Formula
μ = n · p • σ = √(n · p · (1 − p))
Z (without correction) = (k − μ) / σ
Z (with correction) = (k ± 0.5 − μ) / σ
P(a ≤ X ≤ b) ≈ Φ((b + 0.5 − μ)/σ) − Φ((a − 0.5 − μ)/σ)
Continuity correction improves normal approximations to discrete distributions by accounting for the discrete-to-continuous gap.
Frequently Asked Questions
When is continuity correction necessary?
Use it when approximating discrete distributions (e.g., binomial) with the normal distribution, especially for smaller sample sizes.
What if n is very large?
The correction becomes less critical as n grows; both approximations converge.
Can I apply this to Poisson data?
Yes, continuity correction also applies when approximating Poisson counts with the normal distribution.