Final answer:
The shortest living man had the more extreme height when comparing z scores.
Step-by-step explanation:
To compare the heights of the tallest and shortest living men using z scores, we will use the formula z = (x - μ) / σ, where x is the value to be standardized, μ is the mean, and σ is the standard deviation. In this case, the mean height (mean) is 176.99 cm, and the standard deviation is 7.95 cm.
For the tallest man:
- z = (257 - 176.99) / 7.95 = 10.06
For the shortest man:
- z = (44.7 - 176.99) / 7.95 = -16.63
The shortest man has a z-score that is more extreme, since the absolute value of his z-score is larger than that of the tallest man. Therefore, the shortest man's height was more extreme compared to the general population at that time.
We can apply a similar process to deduce the height of other males based on their z-scores. For example, a male with a z-score of 1.27 is 1.27 standard deviations to the right of the mean. If the mean is 170 cm and the standard deviation is 6.28 cm, his height would be 170 + (1.27 * 6.28) = 178.9516 cm. Similarly, a male with a z-score of -2 would be two standard deviations to the left of the mean, indicating his height is shorter than average.