1 - Chapters \( 1=3 \) (Practice Exam) Use z scores to compare the given values. The tallest living man at one time had a height of 226 cm . The shortest living man at that time had a height of 133.3 cm . Heights of men at that time had a mean of 171.41 cm and a Which of these two men had the height that was more extreme? 5.21 of 25 points Since the \( z \) score for the tallest man is \( z=10.54 \) and the \( z \) score for the shortest man is \( z=-7.36 \), the tallest 1 ? man had the height that was more extreme. (Round to two decimal places.)

To determine which of the two men had a height that was more extreme, we can compare their \( z \) scores. The \( z \) score is calculated using the formula: \[ z = \frac{(X - \mu)}{\sigma} \] where: - \( X \) is the value being compared (height in this case), - \( \mu \) is the mean of the distribution, - \( \sigma \) is the standard deviation of the distribution. From the problem, we have: - Height of the tallest man, \( X_1 = 226 \) cm - Height of the shortest man, \( X_2 = 133.3 \) cm - Mean height, \( \mu = 171.41 \) cm - \( z \) score for the tallest man, \( z_1 = 10.54 \) - \( z \) score for the shortest man, \( z_2 = -7.36 \) ### Step 1: Compare the absolute values of the \( z \) scores The absolute value of a \( z \) score indicates how many standard deviations a value is from the mean. The more extreme the height, the larger the absolute value of the \( z \) score. Calculating the absolute values: - For the tallest man: \( |z_1| = |10.54| = 10.54 \) - For the shortest man: \( |z_2| = |-7.36| = 7.36 \) ### Step 2: Determine which \( z \) score is more extreme Now we compare the absolute values: - \( |z_1| = 10.54 \) - \( |z_2| = 7.36 \) Since \( 10.54 > 7.36 \), the tallest man had the height that was more extreme. ### Conclusion Thus, the tallest man had the height that was more extreme.