This statistical method provides an estimate of binomial probabilities using the normal distribution. When dealing with a large number of trials in a binomial experiment, calculating exact probabilities can become computationally intensive. For instance, determining the likelihood of getting at least 60 heads in 100 coin flips is more easily addressed using the normal curve as an approximation rather than summing the probabilities of 60, 61, 62, …, up to 100 heads individually. This process leverages the central limit theorem, which establishes that the binomial distribution approaches a normal distribution as the number of trials increases.
Utilizing the normal distribution in this manner significantly simplifies calculations, offering a practical alternative to complex factorial computations inherent in the binomial formula. Historically, before widespread computing power, this approximation was essential for statisticians and researchers dealing with large datasets. It remains a valuable tool today, particularly in fields like quality control, polling analysis, and risk assessment, providing rapid and reasonably accurate probability estimations. Its efficiency makes it suitable for quick assessments and initial analyses before resorting to more computationally intensive methods if higher precision is required.
