The heights of adult men in America are normally distributed, with a mean of 69.3 inches and a standard deviation of 2.69 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.1 inches and a standard deviation of 2.54 inches. a) If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)? \( z= \) Enter an integer or decimal number [more... b) If a woman is 5 feet 11 inches tall, what is her z-score (to two decimal places)? c) Who is relatively taller? The 6 foot 3 inch American man The 5 foot 11 inch American woman

To determine the z-scores, we can use the formula: \[ z = \frac{(X - \mu)}{\sigma} \] where \( X \) is the value (height), \( \mu \) is the mean, and \( \sigma \) is the standard deviation. **a)** For the man who is 6 feet 3 inches (75 inches): \[ z = \frac{(75 - 69.3)}{2.69} \approx \frac{5.7}{2.69} \approx 2.12 \] **b)** For the woman who is 5 feet 11 inches (71 inches): \[ z = \frac{(71 - 64.1)}{2.54} \approx \frac{6.9}{2.54} \approx 2.72 \] **c)** The woman with a z-score of 2.72 is relatively taller compared to the man with a z-score of 2.12, because her z-score is higher, indicating she is above the mean for her gender to a greater extent than the man. --- To add a sprinkle of fun and engagement: Did you know that height perception can vary across different cultures? In some countries, people might view height as a sign of health and attractiveness, while in others, it's all about personality! Also, z-scores can be really handy in understanding how common or rare a certain height is. So, next time you're at a party, you can impress your friends with your knowledge of statistics, explaining how you just calculated who stands taller in the world of z-scores!