Question

The tallest living man at one time had a height of 262 cm. The shortest living man at that time had a height of 68.6 cm. Heights of men at that time had a mean of 175.32 cm and a standard deviation of 8.17 cm. Which of these two men had the height that was more​ extreme?

Answer 1

Answer:

more the z-score more will be the extreme. therefore tallest man has high extreme

Step-by-step explanation:

Formula for z-score: $\frac{X-\mu }{\sigma}$

where

X is height of tallest man

μ mean height

σ is standard deviation

z score for tallest is

z-score = $\frac{ 262 - 175.32}{8.17} = 10.60$

similarly for shortest man

z-score = $\frac{68.6 - 175.32}{8.17} = - 13.06$

more the z-score more will be the extreme. therefore tallest man has high extreme

Answer 2

Answer:

The shortest living man's height was more extreme.

Step-by-step explanation:

We have been given that the the tallest living man at one time had a height of 262 cm. The shortest living man at that time had a height of 68.6 cm. Heights of men at that time had a mean of 175.32 cm and a standard deviation of 8.17 cm.

First of all, we will find z-scores for both heights suing z-score formula.

$z=\frac{x-\mu}{\sigma}$

$z=\frac{68.6-175.32}{8.17}$

$z=\frac{-106.72}{8.17}$

$z=-13.06$

$z=\frac{x-\mu}{\sigma}$

$z=\frac{262-175.32}{8.17}$

$z=\frac{86.68}{8.17}$

$z=10.61$

Since the data point with a z-score $-13.06$ is more away from the mean than data point with a z-score $10.61$, therefore, the shortest living man's height was more extreme.