Question

Use z scores to compare the given values. The tallest living man at one time had a height of 246 cm. The shortest living man at that time had a height of 75.8 cm. Heights of men at that time had a mean of 174.22 cm and a standard deviation of 7.07 cm. Which of these two men had the height that was more​ extreme?

Since the z score for the tallest man is

and the z score for the shortest man is

the▼

tallest

shortest

man had the height that was more extreme.

Answer 1

Let X be the height of the men                      
X follows normal distribution mean μ and standard deviation σ                      
Given    μ = 174.22 cm       σ = 7.07 cm          
                      
Let X1 = 246       (Height of tallest man)              
z-score for X1 is                      

Let X2 = 75.8       (Height of shortest man)              
z-score for X2 is                      

Since the z-score for the tallest man is 10.15                      
and the z-score for the shortest man is -13.92                      
the                      
shortest                      
man had the height that was more extreme