Continuous probability and normal distributions — Topic Review | Year 12

QUICK RECAP

Connect the ideas

A density is nonnegative and has total area one. Probability is area, not a height.

A continuous variable has probability zero at a single exact value.

Subtract CDF values to find interval probabilities.

Variance is the second moment minus the square of the mean.

Normal notation here is N(mean, variance).

Standardise using the standard deviation of the actual variable, including the smaller standard error for a sample mean.

Independent sums add variances, not standard deviations.

Check sampling assumptions and model limitations before interpreting a calculation.

Complete each paper and show your working.

Practice test 1 — areas and normal models
10 questions · 41 marks · 65 minutes · Technology-assisted
Build from valid densities and interval areas to normal cut-offs, independent totals and sample means.
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Practice test 2 — cumulative models and cut-offs
10 questions · 42 marks · 65 minutes · Technology-assisted
Use changing density shapes, CDFs, reverse normal calculations and weighted measurements.
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Practice test 3 — applications and assumptions
10 questions · 42 marks · 65 minutes · Technology-assisted
Connect polynomial densities with practical normal models and compare totals, averages and model choices.
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Practice test 4 — reverse calculations and comparisons
10 questions · 42 marks · 65 minutes · Technology-assisted
Develop density and CDF reasoning, infer normal parameters, and distinguish correlated readings from independent samples.
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Practice test 5 — modelling and interpretation
10 questions · 43 marks · 75 minutes · Technology-assisted
Work with a two-piece density, compare alternative normal decisions, and evaluate modelling assumptions.
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Practice test 6 — connected applications
10 questions · 47 marks · 75 minutes · Technology-assisted
A more demanding paper joining exact density work, normal parameter inference and independent-sample reasoning.
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