Use mean and standard deviation to fit normal distributions and estimate population percentages with technology.
Interpret z-score direction and absolute distance
Problem
A height has \(z~=~2.1\). Interpret its direction and distance from the population mean in standard deviations.
Big Picture
What this problem is really about
Separate the two jobs of a z-score. Its sign gives direction from the mean—positive above, negative below, and zero at the mean—while its absolute value gives a nonnegative distance measured in standard deviations. Combine both pieces in the contextual interpretation rather than dropping the sign or treating z as a raw measurement.
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