Question

use z scores to compare the given values.
the tallest living man at one time had a height of 246 cm. the shortest living man at that time had a height of 80.8 cm. heights of men at that time had a mean of 171.05 cm and a standard

deviation of 6.91 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.
(round to two decimal places.)

Explanation:

Step1: Calculate the z - score for the tallest man

The formula for the z - score is \(z=\frac{x - \mu}{\sigma}\), where \(x\) is the data value, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.
For the tallest man, \(x = 246\), \(\mu=171.05\), \(\sigma = 6.91\)
\(z=\frac{246-171.05}{6.91}=\frac{74.95}{6.91}\approx10.85\)

Step2: Calculate the z - score for the shortest man

For the shortest man, \(x = 80.8\), \(\mu = 171.05\), \(\sigma=6.91\)
\(z=\frac{80.8 - 171.05}{6.91}=\frac{-90.25}{6.91}\approx - 13.06\)

Step3: Compare the absolute values of the z - scores

The absolute value of the z - score for the tallest man is \(|z_{tallest}|=10.85\)
The absolute value of the z - score for the shortest man is \(|z_{shortest}| = 13.06\)

Answer:

Since the z - score for the tallest man is \(z = 10.85\) and the z - score for the shortest man is \(z=-13.06\), the shortest man had the height that was more extreme.