Z-scores (standardising)
z = (x − μ) / σ. Number of standard deviations a value is from the mean.
Y13 Stats. Standardising lets us use one normal table for any normal distribution. Z > 0: above mean; Z < 0: below; |Z| > 2: unusual.
Worked examples
X ~ N(60, 25); x = 70: z = (70−60)/5 = 2.
z = 2 corresponds to ~97.7% percentile.
Compare exam scores from different distributions via z-score.
Frequently asked questions
Why standardise?
Removes units; comparable across distributions.
Tables or calculator?
Both fine. Modern calculators have NormalCD function.