Question

# Men have heights with a mean of 176 cm and a standard deviation of 7 cm. Charles Darwin had a height of 182 cm. Convert Darwin's height to a z score.

Solution

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Let's use the expression for $z$ score of a population (referring to all men)

$z=\frac{x-\overline{x}}{\sigma} = \frac{6}{7} = 0.86$

where $x-\overline{x}$ is the difference between Darwin's height and the mean height of men, and $\sigma$ is standard deviation of men heights.

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