The continuity correction calculator offers a convenient way to accurately compute exact binomial probabilities and approximate probabilities using the concept of continuity correction. It was designed for statisticians, mathematicians, students, and anyone dealing with binomial probability distributions.

## Calculate continuity correction

### How Does This Calculator Help?

Our calculator simplifies the process of calculating two key types of probabilities:

• Binomial Distribution Probabilities: These are exact probabilities calculated directly from the binomial distribution, based on your inputs for the number of trials, number of successes, and the probability of success in each trial.
• Estimated Probabilities with Continuity Adjustment: These are probabilities approximated using the normal distribution, adjusted for continuity. This method is especially useful for larger datasets and provides a quick estimation that’s close to the exact binomial probabilities.

### How to Use the Continuity Correction Calculator?

Simply enter the total number of trials (n), the number of successful outcomes you’re interested in (x), and the probability of success in a single trial (p). The calculator will then display both the exact probabilities from the binomial distribution and the approximate probabilities using continuity correction.

Whether you’re a student tackling statistics problems, a researcher analyzing data, or just someone curious about probability distributions, our Continuity Correction Calculator is here to provide quick, accurate, and easy-to-understand results.

## What is Continuity Correction?

Continuity correction is a method used in statistics to improve the approximation of a discrete distribution, like the binomial distribution, with a continuous distribution, typically the normal distribution. This technique is particularly useful when dealing with large sample sizes, where the binomial distribution starts to resemble a normal distribution.

### Exact Binomial Probability Formula

The Exact binomial probability can be calculated using the formula:

$$P(X = x) = \binom{n}{x} p^x (1 – p)^{n – x}$$

where $$\binom{n}{x}$$ is the binomial coefficient.

### Approximate Probability with Continuity Correction

For the Approximate probability using continuity correction, you can use the normal approximation to the binomial distribution. The formula is:

$$P(X = x) \approx P(x – 0.5 \leq Z \leq x + 0.5)$$

where $$Z$$ is the standard normal variable. This involves converting $$x$$ into a Z-score and then using the standard normal distribution to find the probability.