Interpretation of a z-score of +2

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Multiple Choice

Interpretation of a z-score of +2

Explanation:
A z-score shows how far a value is from the mean in units of standard deviation. A z-score of +2 means the value lies two standard deviations above the mean, i.e., X = μ + 2σ. This places the score well above the average and indicates it is closer to the upper tail of the distribution; in a standard normal distribution, z = +2 corresponds to about the 97.7th percentile, not “two percentile points” above the mean. It is not twice the mean, since that would imply X = 2μ, and it is not two standard deviations below the mean, which would have a negative sign.

A z-score shows how far a value is from the mean in units of standard deviation. A z-score of +2 means the value lies two standard deviations above the mean, i.e., X = μ + 2σ. This places the score well above the average and indicates it is closer to the upper tail of the distribution; in a standard normal distribution, z = +2 corresponds to about the 97.7th percentile, not “two percentile points” above the mean. It is not twice the mean, since that would imply X = 2μ, and it is not two standard deviations below the mean, which would have a negative sign.

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