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 105.3 cm. Heights of men at that time had a mean of 177.54 cm and a standard deviation of 5.91 cm. Which of these two men had the height that was more​ extreme? Since the z score for the tallest man is zequals nothing and the z score for the shortest man is zequals nothing​, the ▼ tallest shortest man had the height that was more extreme.

Answer 1

For tallest man

Here, μ = 177.54, σ = 5.91 and x = 233. We need to compute P(X <= 233). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (233 - 177.54)/5.91 = 9.38

For smallest man

Here, μ = 177.54, σ = 5.91 and x = 105.3. We need to compute P(X <= 105.3). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (105.3 - 177.54)/5.91 = -12.22

Since the z score for the tallest man is zequals = 9.38 and the z score for the shortest man is zequals-12.22 the ▼ tallest man had the height that was more extreme.