Calculadora de Correção de Continuidade
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
P(X ≤ x) → usa x + 0,5 ; P(X ≥ x) → usa x − 0,5
About this calculator
This calculator applies the continuity correction when approximating a binomial distribution by a normal distribution. When you have a discrete variable (such as number of successes in n trials) and want to use the continuous normal curve to compute probabilities, the continuity correction adjusts the boundaries by adding or subtracting 0.5. This improves accuracy, especially when n is moderate or the probability p is not very close to 0 or 1.
The operation is simple: to compute P(X ≤ x), use the upper adjusted limit x + 0.5; for P(X ≥ x), use x − 0.5; for P(x1 ≤ X ≤ x2), adjust both limits. The calculator converts these values to Z-scores using the binomial mean (n*p) and standard deviation (sqrt(n*p*(1-p))), and then consults the standard normal table to obtain the approximate probability.
Use this tool when you need to estimate binomial probabilities with large n (usually n ≥ 30) and want a quick normal approximation. It is common in hypothesis tests, confidence intervals for proportions, and quality control. The continuity correction is recommended to improve the approximation, reducing the error introduced by treating a discrete distribution as continuous.
Caution: the normal approximation works best when n*p ≥ 5 and n*(1-p) ≥ 5. Even with the correction, accuracy decreases for p close to 0 or 1. Additionally, the continuity correction is more important when n is small or when calculating tail probabilities. Always verify if the approximation is suitable for your problem.
Frequently asked questions
When should I use the continuity correction?
Use it when approximating a binomial distribution by a normal, especially for moderate n (like n between 30 and 100) or when calculating tail probabilities. It improves the accuracy of the approximation.
What is the difference between P(X ≤ x) and P(X < x) in the correction?
In practice, for discrete variables, P(X ≤ x) and P(X < x+1) are equivalent. The standard correction uses x+0.5 for the upper limit, regardless of ≤ or <, because the adjustment compensates for discretization.
Does the continuity correction always improve the approximation?
Generally yes, but the benefit is greater for symmetric distributions and moderate n. For very large n, the correction has little effect; for small n, the normal approximation may not be adequate even with correction.
Can I use this calculator for hypothesis tests about proportions?
Yes, it is common to use the normal approximation with continuity correction in proportion tests, such as the z-test for one proportion or difference of proportions, especially in moderate samples.
What does the Z-score in the output mean?
The Z-score indicates how many standard deviations the adjusted value is above or below the mean. It is used to find the cumulative probability in the standard normal distribution, which approximates the binomial probability.