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NSW Curriculum
NSW Education Standards Authority

11–12Mathematics Standard 11–12 Syllabus

Record of changes
Implementation from 2026
Expand for detailed implementation advice

Content

Year 12 – Standard 2

The normal distribution
Normally distributed datasets
  • Recognise that a dataset that is normally distributed can be represented by a bell-shaped curve

  • Explain that the mean, median and mode are approximately equal for data arising from a random variable that is normally distributed

Calculating z-scores
  • Describe the z-score as the number of standard deviations that a value is above or below the mean
  • Recognise that the set of z-scores for data arising from a random variable that is normally distributed has a mean of 0 and standard deviation of 1
  • Calculate the z-score corresponding to a specific value in a dataset by applying the formula
    z=- μσ, where x is a specific value, μ is the mean and σ is the standard deviation
  • Use z-scores to compare scores from different datasets and justify conclusions in the context of the problem
  • Model and apply the empirical rule, where approximately 68% of data will have z-scores between −1 and 1, approximately 95% of data will have z-scores between −2 and 2, and approximately 99.7% of data will have z-scores between −3 and 3
Probability using z-scores
  • Calculate probabilities using z-scores and the empirical rule
  • Represent probabilities by shading areas under the normal distribution curve

  • Use z-scores to identify probabilities of events less or more extreme than a given event and solve problems
  • Use z-scores to make judgements related to outcomes of a given event or sets of data
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