The z-score formula is z = (x − μ)/σ, where x is the observed value, μ is the population mean, and σ is the population standard deviation. A z-score standardizes a raw value by measuring how many standard deviations it lies above or below the mean. The numerator, x − μ, gives the deviation from the mean. Dividing by σ converts that deviation into standard deviation units. If z is positive, the value is above the mean. If z is negative, the value is below the mean. If z = 0, the value equals the mean. Option B incorrectly adds the value and mean, which does not measure deviation. Option C ignores the mean, and option D ignores the observed value entirely. The z-score is central for normal distribution calculations because it allows values from different scales to be compared using the standard normal distribution. Study Guide references/topics: z-scores, standard normal distribution, mean, standard deviation.

============