

This IB Math AI HL 4.15 – Central Limit Theorem resource develops students’ understanding of how sampling distributions behave and why Normal models appear so widely in statistics. Students explore linear combinations of Normal random variables, independence, and the Central Limit Theorem (CLT), building a clear link between population parameters and the behaviour of sample means. The material connects theory to practical probability calculations involving mixtures, sums, and averages of random variables.
Structured tasks guide learners through finding the mean and variance of linear combinations, modelling totals such as mixtures, and using the CLT to approximate probabilities when the parent distribution is not Normal. Practice and extended problems develop higher-level reasoning about sampling distributions, two-sample differences, and choosing appropriate Normal approximations. With applied contexts and a full answer key, this resource supports HL teaching, IA preparation, and deeper understanding of statistical inference in line with IB Mathematics AI expectations.
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