A z-score measures how many standard deviations a data value is from the mean. The formula is z = (x − μ)/σ, where x is the observed value, μ is the mean, and σ is the standard deviation. Since standard deviation is positive, the sign of the z-score depends on the numerator, x − μ. If x is less than the mean, then x − μ is negative, producing a negative z-score. Therefore, a negative z-score indicates that the observed value is below the mean. A positive z-score indicates a value above the mean, while a z-score of 0 indicates a value exactly equal to the mean. Option D is incorrect because the sign of the z-score gives direct positional information relative to the mean. Study Guide references/topics: z-scores, standard normal distribution, mean, standard deviation.
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