Calculate the Z-score for X = 105, μ = 100, σ = 5.

Calculate the Z-score for X = 105, μ = 100, σ = 5.

• A. 1
• B. 0.5
• C. 2
• D. 1.5

Answer: (A)

A z-score shows how many standard deviations a value is from the mean, so you standardize by subtracting the mean and dividing by the standard deviation. For X = 105 with μ = 100 and σ = 5, compute (105 − 100) / 5 = 5 / 5 = 1. The z-score is 1, meaning 105 is one standard deviation above the mean. The other numbers would correspond to different distances from the mean: a z-score of 0.5 would place X at 102.5, a z-score of 2 would place it at 110, and a z-score of 1.5 would place it at 107.5.

A z-score shows how many standard deviations a value is from the mean, so you standardize by subtracting the mean and dividing by the standard deviation. For X = 105 with μ = 100 and σ = 5, compute (105 − 100) / 5 = 5 / 5 = 1. The z-score is 1, meaning 105 is one standard deviation above the mean. The other numbers would correspond to different distances from the mean: a z-score of 0.5 would place X at 102.5, a z-score of 2 would place it at 110, and a z-score of 1.5 would place it at 107.5.