Question

Use z scores to compare the given values. The tallest living man at one time had a height of 258 cm. The shortest living man at that time had a height of 66.4 cm. Heights of men at that time had a mean of 177.15 cm and a standard deviation of 7.44 cm. Which of these two men had the height that was more extreme? Since the z score for the tallest man is z= and the z score for the shortest man is z=, the man had the height that was more extreme

Answer 1

The z-scores for the tallest and shortest men were calculated relative to the mean height of men at that time; the shortest man had the more extreme z-score.

Step-by-step explanation:

To compare the given values using z-scores, we'll first calculate the z-score for the tallest and shortest living men and then determine which height is more extreme relative to the average height at the time. The formula for the z-score is:

z = (x - μ) / σ

Where:

• x is the value to compare
• μ is the mean of the sample
• σ is the standard deviation

For the tallest man:

z = (258 cm - 177.15 cm) / 7.44 cm = 10.87

For the shortest man:

z = (66.4 cm - 177.15 cm) / 7.44 cm = -14.88

Since the z-score for the tallest man is 10.87 and the z-score for the shortest man is -14.88, the shortest man had the height that was more extreme.