m-tall-and-is-this-individual-in-the-top-25-tail-according-to-the-empirical-rule

Question

If heights in a population are approximately normal with mean 170 cm and standard deviation 8 cm, what is the approximate z-score for an individual 186 cm tall and is this individual in the top ~2.5% tail according to the empirical rule?

Accepted Answer

z = +2.0, and yes — approximately in the top 2.5%.

Answer

z = +3.0, so the individual is in the top 0.15%, which is much rarer than 2.5%.

Answer

z = +1.5, which places the person around the top 6.7%, so not in the top 2.5%.

Answer

z = +2.0, and no — z = +2 only indicates the 50th percentile above the mean and cannot identify the tail proportion without exact z-tables.