Step 1 :Given that the mean height of the group of men is \(169 \mathrm{~cm}\), the standard deviation is \(7 \mathrm{~cm}\), and Jordan's height is \(187 \mathrm{~cm}\).
Step 2 :The z-score is a measure of how many standard deviations an element is from the mean. To calculate the z-score of Jordan's height, we subtract the mean from his height and then divide by the standard deviation.
Step 3 :Subtract the mean height from Jordan's height: \(187 - 169 = 18\).
Step 4 :Divide the result by the standard deviation: \(\frac{18}{7} = 2.5714285714285716\).
Step 5 :Round the result to the nearest thousandths to get the z-score: \(2.571\).
Step 6 :Final Answer: The z-score for Jordan's height is approximately \(\boxed{2.571}\).
Step 7 :Since the z-score is greater than 2, Jordan's height is considered unusual in this group of men.