What is the formula for the z-score of a value x in a distribution with mean μ and standard deviation σ?

• A. z = (μ - x) / σ
• B. z = (x - σ) / μ
• C. z = (x + μ) / σ
• D. z = (x - μ) / σ

Answer: (D)

Z-scores measure how far a value is from the mean in units of the standard deviation. To do this, you center the value by subtracting the mean, then scale by dividing by the standard deviation. This gives z = (x − μ) / σ. When x equals the mean, z is 0; when x is one standard deviation above the mean, z is 1; two standard deviations below the mean, z is −2. The other forms don’t standardize in the same way: reversing the subtraction flips the sign, and using μ or adding the mean before dividing doesn’t scale by the spread of the distribution.