Given a control result of 105, an expected mean of 100, and a standard deviation of 4 for the control material, what is the Z-score?

Given a control result of 105, an expected mean of 100, and a standard deviation of 4 for the control material, what is the Z-score?

• A. 0.75
• B. 1.25
• C. 2.0
• D. 5.0

Answer: (B)

You’re being tested on standardizing a value using a Z-score, which expresses how far an observed result is from the mean in units of the standard deviation. Compute (observed − mean) ÷ standard deviation: (105 − 100) ÷ 4 = 5 ÷ 4 = 1.25. So the Z-score is 1.25, meaning the control result sits 1.25 standard deviations above the mean. The other numbers would correspond to different distances from the mean (for example, 2.0 is two standard deviations above, 5.0 is five SDs, etc.).

You’re being tested on standardizing a value using a Z-score, which expresses how far an observed result is from the mean in units of the standard deviation. Compute (observed − mean) ÷ standard deviation: (105 − 100) ÷ 4 = 5 ÷ 4 = 1.25. So the Z-score is 1.25, meaning the control result sits 1.25 standard deviations above the mean. The other numbers would correspond to different distances from the mean (for example, 2.0 is two standard deviations above, 5.0 is five SDs, etc.).