Normal Distribution & Z-score
Convert to z-scores and find probabilities and percentiles under the bell curve, with the standardizing step and table lookup shown. Try “P(X > 65) when mean = 50, sd = 10”.
Try an example:
How the Normal Distribution & Z-score works
- Standardize: z = (x − μ) ÷ σ = (65 − 50) ÷ 10 = 1.5.
- Look up or compute the area to the left of z.
- For “greater than”, subtract from 1 (P ≈ 0.0668).
Frequently asked questions
What is a z-score?
The number of standard deviations a value is from the mean.
What is the 68-95-99.7 rule?
About 68%, 95% and 99.7% of values lie within 1, 2 and 3 standard deviations of the mean.
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