Question

The tallest living man at one time had a height of 230 cm. The shortest living man at that time had a height of 91.3 cm. Heights of men at that time had a mean of 170.53 cm and a standard deviation of 5.91 cm. Which of these two men had the height that was more​ extreme?

Answer 1

Answer: The shortest living man at that time had the height that was more​ extreme.

Step-by-step explanation:

We will z scores to solve this exercise. The formula we need is:

 $z=\frac{x-\mu}{\sigma}$

Where $x$ is the raw score, $\mu$ is the mean and $\sigma$ is the standard deviation.

We know at that time heights of men had a mean of 170.53 centimeters and a standard deviation of 5.91 centimeters, then:

$\u=170.53\\\\\sigma=5.91$

Knowing that the tallest living man at that time had a height of 230 centimeters, we get:

$z=\frac{230-170.53}{5.91}\approx10.07$

And knowing that the shortest living man at that time had a height of 91.3 centimeters, we get:

$z=\frac{91.3-170.53}{5.91}\approx-13.40$

Based on this, we can conclude that the shortest living man at that time had the height that was more​ extreme.