In this problem, and in general statistics, z represents the standard score of the data.
This standard score is the number of standard deviations that there are above or below a sample.
We have the mean: 173.38 cm
and the standard deviation: 8.78 cm
We first determined the standard score for the tallest living man:
We obtain the difference between this sample and the mean:
[tex]a=260cm\text{ -173.38cm=86.62cm}[/tex]Then we calculate how many standard deviations are in this difference:
[tex]z=\frac{86.62}{8.78}=9.87[/tex]Then the standard score for the tallest living man is 9.87
We need to do the same to the shortest living man:
[tex]b=108.6cm-173.38\text{ cm=}-64.78cm[/tex]Remember that if the sample is minor than the mean we take the absolute value.
Then the standard score:
[tex]z=\frac{64.78}{8.78}=7.38[/tex]Then the standard score for the shortest living man is 7.38
The height that was more extreme is the height that has a standard score major, then we can conclude:
The standard score for the tallest living man is 9.87
The standard score for the shortest living man is 7.38
And the height that was more extreme is the tallest living man's height