📐 Normal Approximation Calculator
Estimate binomial probabilities using the normal approximation with continuity correction — useful when the number of trials is too large to compute exactly by hand.
What the normal approximation is for
When the number of trials in a binomial situation gets large, calculating exact probabilities by hand becomes impractical. The normal approximation lets you treat a binomial distribution as approximately normal, using its mean (n x p) and standard deviation, which is accurate when both n x p and n x (1-p) are reasonably large (commonly at least 5-10).
How this calculator works
Enter the number of trials, the probability of success on each trial, and the threshold value you’re interested in. Choose whether you want the probability of getting at most or at least that many successes. The calculator applies a continuity correction (adjusting the threshold by 0.5) before converting it to a z-score, which improves accuracy since it approximates a discrete distribution with a continuous one.
This approximation becomes less reliable when p is very close to 0 or 1, or when n is small. For those cases, an exact binomial calculation is more appropriate. Provided for general educational purposes.