Question

The tallest living man at one time had a height of 265 cm. The shortest living man at that time had a height of 109.1 cm. Heights of men at that time had a mean of 173.73 cm and a standard deviation of 8.65 cm. Which of these two men had the height that was more​ extreme?

Answer 1

The tallest living man at one time had a more extreme height compared to the shortest living man at that time.

Step-by-step explanation:

In this question, we are given the heights of the tallest and shortest living men at a specific time, as well as the mean and standard deviation of heights at that time. To determine which man had a more extreme height, we need to compare their heights to the mean and see how many standard deviations away they are.

The tallest man had a height of 265 cm, which is 265 - 173.73 = 91.27 cm above the mean.

The shortest man had a height of 109.1 cm, which is 173.73 - 109.1 = 64.63 cm below the mean.

Since the tallest man's height is significantly farther away from the mean compared to the shortest man's height, we can conclude that the tallest man had a more extreme height.

Answer 2

tallest man height is more extreme.

Step-by-step explanation:

Given:

Heights of men at that time had a mean of 173.73 cm and a standard deviation of 8.65 cm.

Concept used:

Convert height into z scores for comparison of deviation from the mean.

Solution:

Tallest man height = 265 cm

`Z_(tall) =(265-173.73)/(8.65) \\=10.55`

Shortest man height = 109.1 cm

`Z_(short) =(109.1-173.73)/(8.65) \\=-7.47`

Thus we find that tallest man is 10.55 std deviations from the mean to the right and shortest man is 7.47 std deviations from the mean to the left.

Hence tallest man height is more extreme.