

This IB Math AI SL 4.9 – Normal Distribution resource builds students’ understanding of how continuous data are modelled using the normal distribution and interpreted through technology. Students develop fluency with normal notation (X \sim N(\mu,\sigma)), the bell-shaped curve, and the roles of mean and standard deviation in describing centre and spread. The Empirical Rule is used to estimate probabilities, while calculator functions such as NormalCDF and NormalInv support exact probability calculations, percentiles, and cut-off values in real contexts like IQ scores, manufacturing tolerances, heights, and test results .
Structured tasks progress from core concepts and graph interpretation to standardising values with z-scores, calculating tail and interval probabilities, and solving inverse normal problems. Students interpret probabilities in context and connect graphical, numerical, and algebraic representations. Extended exam-style problems develop deeper reasoning, including modelling with unknown parameters, using normal models for quality control decisions, and working with the distribution of differences of independent normal variables. With scaffolded practice, technology integration, challenging extension tasks, and a full answer key, this resource supports SL classroom instruction and independent study in line with IB Mathematics AI expectations.
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