Coaching Centre
Chapter 8: The Normal Distribution Notes
Normally distributed data and its properties, the 68-95-99.7 rule, z-scores, comparing scores from different datasets, and applications including percentages and quality control.
Sections
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8A Normally distributed data Mastered
What normally distributed data looks like, the properties of the normal curve, real examples, and how to recognise data that is not normal.
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8B The 68–95–99.7 rule Mastered
The empirical rule for normal distributions: about 68%, 95% and 99.7% of data lie within 1, 2 and 3 standard deviations of the mean, and using the symmetric pieces to find percentages.
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8C z-scores Mastered
Calculating a z-score as the number of standard deviations a score is from the mean, interpreting positive, negative and zero z-scores, and identifying unusual scores.
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8D Converting and comparing with z-scores Mastered
Converting a z-score back to a raw score, comparing performances across different tests using z-scores, and finding percentages from whole-number z-scores.
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8E Applications and quality control Mastered
Solving practical problems with normal distributions: percentages and numbers of items, setting cut-offs, and using the mean and standard deviation for quality control in manufacturing.