Question

The tallest living man at one time had a height of 250 cm. The shortest living man at that time had a height of 72.5 cm. Heights of men at that time has a of 172.89 cm and a standard deviation of 7.09cm. Which of these two men had the height that was more extreme

Answer 1

Using z-scores, it is found that the shortest men had a height that was more extreme.

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The z-score of a score X in a set with mean $\mu$ and standard deviation $\sigma$ is given by:

$Z = \frac{X - \mu}{\sigma}$

• It measures how many standard deviations X is above or below the mean.
• The higher |Z|, the more extreme the measure X is.

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• Mean of 172.89 cm, thus $\mu = 172.89$
• Standard deviation of 7.09 cm, thus $\sigma = 7.09$

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For the men with a height of 250cm, the z-score is:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{250 - 172.89}{7.09}$

$Z = 10.88$

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For the men with a height of 72.5cm, the z-score is:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{72.5 - 172.89}{7.09}$

$Z = -14.16$

|Z| = -14.16

Due to the higher absolute value of the z-score, the shortest men had a height that was more extreme.

A similar problem is given at https://brainly.com/question/16902257