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The normal distribution and z-scores
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Learn it z = (x − μ)/σ tells how many standard deviations x is from the mean. About 68% of values are within 1σ, 95% within 2σ and 99.7% within 3σ. Use z to find probabilities from a table or calculator.
Example: Heights: μ = 170 cm, σ = 8 cm. P(height > 186)?
- z = (186 − 170)/8 = 2.
- P(Z > 2) ≈ 0.023 (about 2.3%).
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