If a control mean is 100 and SD is 5, a result of 95 yields Z = (95-100)/5 = -1. Which statement is true?

If a control mean is 100 and SD is 5, a result of 95 yields Z = (95-100)/5 = -1. Which statement is true?

• A. The Z-score is 0.
• B. The Z-score is -2.
• C. The Z-score is -1.
• D. The Z-score is -0.5.

Answer: (C)

Z-scores measure how far an observation is from the mean in units of standard deviation. Compute as (observed − mean) ÷ standard deviation: (95 − 100) ÷ 5 = −5 ÷ 5 = −1. So the Z-score is −1, meaning the result is one standard deviation below the mean. This aligns with the true statement. To see why the other values wouldn’t fit: a Z of 0 would require the observation to be the mean (100). A Z of −2 would place the value at 90 (100 + −2 × 5). A Z of −0.5 would place it at 97.5 (100 + −0.5 × 5).

Z-scores measure how far an observation is from the mean in units of standard deviation. Compute as (observed − mean) ÷ standard deviation: (95 − 100) ÷ 5 = −5 ÷ 5 = −1. So the Z-score is −1, meaning the result is one standard deviation below the mean. This aligns with the true statement.

To see why the other values wouldn’t fit: a Z of 0 would require the observation to be the mean (100). A Z of −2 would place the value at 90 (100 + −2 × 5). A Z of −0.5 would place it at 97.5 (100 + −0.5 × 5).