A tool that facilitates the estimation of binomial probabilities using the normal distribution. This becomes particularly useful when dealing with large sample sizes in binomial experiments. For instance, calculating the probability of obtaining a specific number of successes in a large series of independent trials, each with a fixed probability of success, can be computationally intensive using the binomial formula directly. This method offers a simplified approach by leveraging the properties of the normal distribution.
This approximation method offers significant advantages in situations where direct binomial calculations are cumbersome or impractical. It provides a relatively accurate estimate, particularly when both np and n(1-p) are sufficiently large (typically greater than or equal to 5), where n represents the number of trials and p the probability of success. Historically, this technique gained prominence before the widespread availability of computing power, as it allowed statisticians and researchers to analyze large datasets more efficiently. Its continued relevance stems from its intuitive application and ability to provide quick, reliable probability estimates.
