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Sagot :
Answer:
Step-by-step explanation:
To compare the heights of the tallest and shortest living men using z-scores, we need to calculate the z-score for each height and then determine which one is more extreme.
Given information:
Tallest man's height: 232 cm
Shortest man's height: 145.2 cm
Mean height: 176.81 cm
Standard deviation: 5.16 cm
Step 1: Calculate the z-score for the tallest man's height.
z-score = (Tallest man's height - Mean height) / Standard deviation
z-score = (232 cm - 176.81 cm) / 5.16 cm
z-score = 10.74
Step 2: Calculate the z-score for the shortest man's height.
z-score = (Shortest man's height - Mean height) / Standard deviation
z-score = (145.2 cm - 176.81 cm) / 5.16 cm
z-score = -6.10
Step 3: Determine which height is more extreme.
The absolute value of the z-score indicates how many standard deviations the value is from the mean. The larger the absolute value of the z-score, the more extreme the value.
In this case, the absolute value of the z-score for the tallest man's height (10.74) is larger than the absolute value of the z-score for the shortest man's height (6.10).
Therefore, the tallest man's height is more extreme compared to the shortest man's height.
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