Interpret a z-score of 2.0 in a standard normal distribution.

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Multiple Choice

Interpret a z-score of 2.0 in a standard normal distribution.

Explanation:
A z-score of 2.0 shows the value is two standard deviations above the mean. In a standard normal distribution, being two standard deviations above corresponds to the cumulative area up to that point of about 0.977, or the 97.7th percentile. So the interpretation is that the value lies well above the mean, with about 97.7% of observations falling at or below it. For context, a z-score of +2 is not the same as the 84th percentile (which is about z = +1) and certainly not the 97.7th percentile from a negative direction (which would occur if the value were two standard deviations below the mean, around the 2.5th percentile).

A z-score of 2.0 shows the value is two standard deviations above the mean. In a standard normal distribution, being two standard deviations above corresponds to the cumulative area up to that point of about 0.977, or the 97.7th percentile. So the interpretation is that the value lies well above the mean, with about 97.7% of observations falling at or below it.

For context, a z-score of +2 is not the same as the 84th percentile (which is about z = +1) and certainly not the 97.7th percentile from a negative direction (which would occur if the value were two standard deviations below the mean, around the 2.5th percentile).

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