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Year 12 · Statistics & Probability
Normal distribution and z-scores
A z-score says how many standard deviations a value is from the mean. About 68% of values lie within 1 SD, 95% within 2, 99.7% within 3.
How to do it
- z = (value − mean) ÷ SD.
- Positive z is above the mean, negative below.
Worked example
Scores are normally distributed with mean 50 and standard deviation 10. About what percentage of scores lie between 20 and 80?
20 to 80 is 3 standard deviations either side of the mean. By the 68–95–99.7 rule that is about 99.7%.
Answer: 99.7
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Watch outDivide by the standard deviation, not the variance.
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