IB Maths AA SL 4.9 - The Normal Distribution

This IB Maths AA SL Topic 4.9 – The Normal Distribution resource develops students’ understanding of continuous probability distributions and their applications. It begins by introducing the normal distribution as a symmetrical, bell-shaped distribution described by its mean and standard deviation. Students explore how changing the mean shifts the distribution, how changing the variance affects its spread, and how the empirical rule describes the proportions of data lying within one, two, and three standard deviations of the mean.

The lesson then develops confidence in performing normal probability calculations using the cumulative distribution function, including probabilities below a value, above a value, and between two values. Students also learn how to use inverse normal calculations to find values associated with given percentiles or tail probabilities. The resource includes contextual applications involving IQ scores, manufacturing tolerances, and human heights, alongside detailed calculator instructions for the TI-Nspire CX/CX II and Casio fx-CG50. With clear diagrams, worked examples, empirical-rule reasoning, technology guidance, probability calculations, and fully worked solutions, this resource helps SL students build strong statistical modelling skills in line with IB Mathematics AA expectations.