Use z scores to compare the given values.
The tallest living man at one time had a height of $228 \mathrm{~cm}$. The shortest living man at that time had a height of $112.7 \mathrm{~cm}$. Heights of men at that time had a mean of $174.08 \mathrm{~cm}$ and a standard deviation of $5.22 \mathrm{~cm}$. Which of these two men had the height that was more extreme?

Since the $z$ score for the tallest man is $z=\square$ and the $z$ score for the shortest man is $z=\square$, the $\square \square$ man had the height that was more extreme. (Round to two decimal places.)
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Step 1 ：Given the mean height of men at that time was \(174.08 \mathrm{~cm}\), the standard deviation was \(5.22 \mathrm{~cm}\), the tallest man's height was \(228 \mathrm{~cm}\), and the shortest man's height was \(112.7 \mathrm{~cm}\).

Step 2 ：The z-score is calculated by subtracting the mean from the value and then dividing by the standard deviation.

Step 3 ：For the tallest man, the z-score is calculated as \((228 - 174.08) / 5.22\), which gives a z-score of \(10.33\).

Step 4 ：For the shortest man, the z-score is calculated as \((112.7 - 174.08) / 5.22\), which gives a z-score of \(-11.76\).

Step 5 ：The z-score tells us how many standard deviations a value is from the mean. The sign of the z-score tells us whether the value is above (positive) or below (negative) the mean.

Step 6 ：Comparing the absolute values of the z-scores, we find that the shortest man's height is more extreme, as \(|-11.76| > |10.33|\).

Step 7 ：Final Answer: Since the z score for the tallest man is \(z=\boxed{10.33}\) and the z score for the shortest man is \(z=\boxed{-11.76}\), the \(\boxed{\text{shortest}}\) man had the height that was more extreme.