In a standard normal distribution, z-score for the mean = ?

A z-score measures how many standard deviations a value is above or below 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. If the observed value equals the mean, then x = μ. Substituting into the formula gives z = (μ − μ) / σ = 0 / σ = 0. Therefore, the z-score corresponding to the mean is always 0 in any normal distribution, including the standard normal distribution. In the standard normal distribution specifically, the mean is 0 and the standard deviation is 1, so the mean lies exactly at z = 0. A z-score of 1 would indicate one standard deviation above the mean, and −1 would indicate one standard deviation below the mean. Study Guide references/topics: standard normal distribution, z-scores, mean, standard deviation.

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