Question

use z scores to compare the given values. the tallest living man at one time had a height of 243 cm. the shortest living man at that time had a height of 132.2 cm. heights of men at that time had a mean of 175.38 cm and a standard deviation of 6.25 cm. which of these two men had the height that was more extreme? since the z score for the tallest man is z = and the z score for the shortest man is z =, the man had the height that was more extreme. (round to two decimal places.)

Explanation:

Step1: Recall z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step2: Calculate z - score for the tallest man

Given $x = 243$ cm, $\mu=175.38$ cm, and $\sigma = 6.25$ cm.
$z_1=\frac{243 - 175.38}{6.25}=\frac{67.62}{6.25}=10.82$

Step3: Calculate z - score for the shortest man

Given $x = 132.2$ cm, $\mu = 175.38$ cm, and $\sigma=6.25$ cm.
$z_2=\frac{132.2-175.38}{6.25}=\frac{- 43.18}{6.25}=-6.91$

Step4: Compare the absolute values of z - scores

The absolute value of $z_1$ is $|z_1| = 10.82$ and the absolute value of $z_2$ is $|z_2|=6.91$. Since $10.82>6.91$, the tallest man has a more extreme height.

Answer:

Since the z - score for the tallest man is $z = 10.82$ and the z - score for the shortest man is $z=-6.91$, the tallest man had the height that was more extreme.