Question

use z scores to compare the given values. the tallest living man at one time had a height of 249 cm. the shortest living man at that time had a height of 38.9 cm. heights of men at that time had a mean of 173.34 cm and a standard deviation of 8.23 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 $x = 249$ cm, $\mu=173.34$ cm, $\sigma = 8.23$ cm. Then $z_1=\frac{249 - 173.34}{8.23}=\frac{75.66}{8.23}\approx9.20$.

Step3: Calculate z - score for the shortest man

Given $x = 38.9$ cm, $\mu = 173.34$ cm, $\sigma=8.23$ cm. Then $z_2=\frac{38.9 - 173.34}{8.23}=\frac{- 134.44}{8.23}\approx - 16.34$.

Step4: Compare the absolute values of z - scores

The absolute value of $z_1$ is $|z_1|=9.20$ and the absolute value of $z_2$ is $|z_2| = 16.34$. Since $16.34>9.20$, the shortest man has a more extreme height.

Answer:

Since the z - score for the tallest man is $z = 9.20$ and the z - score for the shortest man is $z=-16.34$, the shortest man had the height that was more extreme.