§-Quick questions
NSWMaths Standard 2Year 12: Statistical Analysis
Quick questions on The normal distribution and the empirical rule for HSC Maths Standard 2
3short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.
What is the normal distribution?Show answer
The normal distribution (or bell curve) is a smooth curve that shows how data is spread out. It turns up naturally whenever a quantity is built from many small, separate effects added together. Common examples are adult heights, exam scores across a large group, repeated measurement errors, and the fill weight of mass-produced bottles. Its shape is set entirely by two numbers:
What is the empirical rule, band by band?Show answer
The empirical rule is the main result here. Do not just memorise three separate numbers. Instead, build the rule up one band at a time, because that is exactly how the harder questions are set out step by step. The diagrams below shade one more standard-deviation band at each stage.
What is the tails, by symmetry?Show answer
The single most useful follow-up move is splitting "inside the band" into "outside the band", then halving for one tail. If is inside , then is outside, and by symmetry each tail carries half:
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