The Standard Normal Distribution

Students read and sketch a normal curve, identify the mean and standard deviation from a context, and use the empirical (68-95-99.7) rule to estimate probabilities.

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Learning objective overview

Master Teaching Guide coverage for this objective.

Current NZC (2007)
  • No direct alignment recorded
New NZC (2026)
  • NZC26-P4-PRO-ETP-K-Y9-08

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Terminology

    Task goals

    • Foundation: Students read and sketch a normal curve, identify the mean and standard deviation from a context, and use the empirical (68-95-99.7) rule to estimate probabilities.
    • Proficient: Students calculate a z-score from raw data and use technology or standard normal tables to find probabilities such as $P(X < a)$, $P(X > a)$, and $P(a < X < b)$.
    • Excellence: Students solve inverse-normal problems (finding a raw value or boundary given a probability), combine normal-distribution reasoning with real NCEA-style contexts, and justify assumptions about normality.

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    The Standard Normal Distribution

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