Support · Mathematics Extension 1 11–12 – Year 12 · The binomial distribution and sampling distribution of the mean
Support State the central limit theorem as: for a population with mean μ and variance σ², provided the sample size n is large enough (n ≥ 30), the sampling distribution is approximately normal with mean μ and variance σ²/n; that is, X̅ is approximately N(μ,σ²/n)
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Prerequisite dot points
Apply the empirical rule to make judgements and solve problems involving probabilities of normally distributed data: that for normal distributions, approximately 68% of data lie within one standard deviation of the mean, approximately 95% within two standard deviations of the mean and approximately 99.7% within three standard deviations of the mean
Mathematics Advanced 11–12 – Year 12 · Random variables Draft mapping
No checked resources on this prerequisite dot point yet.
Distinguish between a standard normal distribution with mean 0 and standard deviation 1, and the non-standard normal distribution with mean μ and standard deviation σ
Mathematics Advanced 11–12 – Year 12 · Random variables Draft mapping
No checked resources on this prerequisite dot point yet.
Identify the graph of the probability density function of a normal distribution, the normal curve, as an ‘ideal’ bell-shaped curve, symmetrical about its mean which is equal to its mode and median, and as having most values concentrated about the mean
Mathematics Advanced 11–12 – Year 12 · Random variables Draft mapping
No checked resources on this prerequisite dot point yet.