A particular group of men have heights with a mean of $169 \mathrm{~cm}$ and a standard deviation of $7 \mathrm{~cm}$. Jordan had a height of $187 \mathrm{~cm}$.
a) Convert Jordan's height to a z-score. (Round to the nearest thousandths)
b) Is Jordan's height unusual?
Answer
Since the z-score is greater than 2, Jordan's height is considered unusual in this group of men.
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.
