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Z = (x − μ) / σ. A z-score tells how many standard deviations a value is from the mean. Z=0: at the mean. Z=1: one SD above (84th percentile). Z=−1: one SD below (16th percentile). Z=1.96: 97.5th percentile (used in 95% CIs). Assumes a normal distribution—z-scores have less meaning for skewed distributions. Used for outlier detection, standardizing test scores, and quality control.
z = 1.2500