Which statement is true when a Z-score equals 3?

Which statement is true when a Z-score equals 3?

• A. It indicates three standard deviations below the mean.
• B. It indicates the value is three standard deviations away from the mean in either direction.
• C. It indicates the value is three standard deviations above the mean.
• D. It indicates the mean is three times the standard deviation.

Answer: (C)

A z-score shows how many standard deviations a value is from the mean, with positive values meaning above the mean. If the z-score is 3, the value sits 3 standard deviations above the mean (X = μ + 3σ). This places it in the far right tail of the distribution, far from the average. The idea of being three standard deviations away in either direction would apply to the magnitude |z| = 3, not to a z-score of exactly +3. Being three standard deviations below the mean would correspond to z = −3, and a mean being three times the standard deviation isn’t related to this measure.

A z-score shows how many standard deviations a value is from the mean, with positive values meaning above the mean. If the z-score is 3, the value sits 3 standard deviations above the mean (X = μ + 3σ). This places it in the far right tail of the distribution, far from the average.

The idea of being three standard deviations away in either direction would apply to the magnitude |z| = 3, not to a z-score of exactly +3. Being three standard deviations below the mean would correspond to z = −3, and a mean being three times the standard deviation isn’t related to this measure.