Continuity Correction Calculator

What Is Continuity Correction?

Continuity correction adjusts a discrete count so you can approximate it with a continuous normal distribution. When you use a normal curve to estimate binomial probabilities, adding or subtracting $0.5$ to the integer boundary improves the approximation.

Continuity Correction Rules

Let $X$ be binomial and $Y$ the normal approximation. Common replacements are:

• $P(X = n) \approx P(n - 0.5 < Y < n + 0.5)$
• $P(X \le n) \approx P(Y < n + 0.5)$
• $P(X < n) \approx P(Y < n - 0.5)$
• $P(X \ge n) \approx P(Y > n - 0.5)$
• $P(X > n) \approx P(Y > n + 0.5)$

The approximating normal uses mean $\mu = Np$ and standard deviation $\sigma = \sqrt{Np(1-p)}$.

When to Use It

The normal approximation to the binomial is usually reasonable when both $Np \ge 5$ and $N(1-p) \ge 5$ (some texts use 10). Continuity correction is especially helpful for moderate sample sizes where the discrete nature of $X$ still matters.

How to Use This Calculator

• Enter the number of trials $N$.
• Enter the number of successes $n$.
• Enter the success probability $p$ (between 0 and 1).
• Choose the probability statement to correct.
• Read the corrected interval and the normal-approximated probability.

Related Tools

Explore related probability tools:

• Binomial Probability Distribution Calculator
• Normal Distribution Calculator
• Central Limit Theorem Calculator