Normal Approximation for the Sampling Distribution of a Proportion

This GeoGebra example visualizes how the sampling distribution of the sample proportion can be approximated by a Normal distribution when parameters n and p are given. It demonstrates the match (and when it may fail) between the discrete Binomial proportion probabilities and a continuous Normal curve using the standard mean np and standard deviation sqrt(npq). The construction uses Sequence to generate the list of possible proportions (propList), binomProb to compute Binomial probabilities at each proportion value, and BarChart to display the discrete probability mass. It then overlays a Normal approximation via Normal together with computed quantities m, sd, np, and nq, producing objects such as norm1/norm2 and propDensity. A fit step (fit) and several text annotations (text1–text6) highlight the approximation conditions and the resulting comparison. Suitable for secondary to early undergraduate courses on probability and statistics, and for classroom demonstrations of the normal approximation to the distribution of proportions.