91影视

The mean height of men is given as 174.12 cm, and the standard deviation of the heights of men is equal to 7.10 cm.

Thez-score is the value that explains the location of a given data value from the mean value in terms of the standard deviation. Mathematically,

$Z=\frac{x-\stackrel{炉}{x}}{s}$

Values with a greater z-score (in absolute terms) are said to be less extreme compared to values with a smaller z-score.

The z-score for the tallest man with a height equal to 251 cm is computed as follows:

$$\begin{gathered} z=\frac{x-\stackrel{炉}{x}}{s} \\ =\frac{251-174.12}{7.10} \\ =10.83 \end{gathered}$$

Therefore, thez-score for the tallest man with a height equal to 251 cm is equal to 10.83.

The z-score for the shortest man with a height equal to 54.6 cm is computed as follows:

$$\begin{gathered} z=\frac{x-\stackrel{炉}{x}}{s} \\ =\frac{54.6-174.12}{7.10} \\ =-16.83 \end{gathered}$$

Therefore, thez-score for the tallest man with a height equal to 54.6 cm is equal to -16.83.

The height of the tallest man is 10.83 standard deviations above the mean, and the height of the shortest man is 16.83 standard deviations below the mean.

As 54.6 cm is farther from the mean value compared to 251 cm, theshortest man鈥檚 height, equal to 54.6 cm, ismore extreme than the tallest man鈥檚 height.