With mean 100 and SD 5, a result of 85 yields Z = -3. Which statement is true?

With mean 100 and SD 5, a result of 85 yields Z = -3. Which statement is true?

• A. The Z-score is -2.
• B. The Z-score is -1.
• C. The Z-score is 3.
• D. The Z-score is -3.

Answer: (D)

Z-scores tell you how many standard deviations a value is from the mean, using Z = (X − μ)/σ. With X = 85, μ = 100, and σ = 5, the calculation is Z = (85 − 100)/5 = −15/5 = −3. The negative sign shows the value is below the mean, and the magnitude 3 indicates three standard deviations away. So the correct statement is that the Z-score is −3. For context, a Z-score of −2 would correspond to 90, and −1 to 95, while a Z-score of 3 would correspond to 115, none of which match the given data.

Z-scores tell you how many standard deviations a value is from the mean, using Z = (X − μ)/σ. With X = 85, μ = 100, and σ = 5, the calculation is Z = (85 − 100)/5 = −15/5 = −3. The negative sign shows the value is below the mean, and the magnitude 3 indicates three standard deviations away. So the correct statement is that the Z-score is −3. For context, a Z-score of −2 would correspond to 90, and −1 to 95, while a Z-score of 3 would correspond to 115, none of which match the given data.