A z-score of 2 means the observation is how many standard deviations above the mean?

• A. Two standard deviations above the mean.
• B. The same as the observation's difference from the mean in raw units.
• C. The square root of the mean.
• D. A z-score has no relation to standard deviations.

Answer: (A)

Z-scores express where an observation sits relative to the distribution in units of standard deviations. The z-score is computed as (X − μ)/σ, so if the z-score is 2, the observation is two standard deviations above the mean: X = μ + 2σ. The raw difference X − μ is in original units, not in standard deviation units, which is why it’s not the right interpretation. The square root of the mean has no relation to z-scores, and a z-score is defined precisely in terms of standard deviations, so that option is incorrect.