Approximation of Binomial, Poisson, and Normal Distributions

This interactive GeoGebra app demonstrates the approximation relationships among the binomial (B), Poisson (Po), and normal (N) distributions. It visually shows how a binomial distribution can be approximated by a Poisson distribution when n is large and p is small, and by a normal distribution when n is large and p is not too extreme; it also shows the normal approximation to the Poisson distribution for large λ. The core mathematical concepts include discrete probability distributions (binomial and Poisson), continuous normal distribution, expected value, variance, standard deviation, and the limiting theorems (Poisson theorem and central limit theorem). The construction uses GeoGebra commands such as BinomialDist, Poisson, Normal, and Segment, with sliders to adjust parameters n, p, and λ, and text objects to display np and npq. This app is suitable for high school or undergraduate statistics courses, serving as a visual aid for teaching distribution approximations and as a tool for exploratory data analysis.