Question

Use z scores to compare the given values. The tallest living man at one time had a height of 233 cm. The shortest living man at that time had a height of 74.5 cm. Heights of men at that time had a mean of 176.75 cm and a standard deviation of 6.24 cm. Which of these two men had the height that was more extreme?

Answer 1

Given:

The tallest living man at one time had a height of 233 cm. The shortest living man at that time had a height of 74.5 cm. Heights of men at that time had a mean of 176.75 cm and a standard deviation of 6.24 cm.

Required:

We need to find that which man had the height that was more​ extreme

Step-by-step explanation:

The formula for z-score is

`z-score=(X-\mu)/(\sigma)`

where

`\begin{gathered} X\text{ is hirght} \\ \mu\text{ is mean} \\ \sigma\text{ is standard deviation} \end{gathered}`

put the values for tallest

`z=(233-176.75)/(6.24)=9.01`

now for shortest

`x=(74.5-176.75)/(6.24)=-16.39`

more the z-score more will be the extreme.

Final answer:

z-score for talles is 9.01

z-score for shortest is -16.39

and the extreme is tallest men