The heights of adult men in America are normally distributed, with a mean of 69.2 inches and a standard deviation of 2.64 inches. The heights of adult wormen in America are also normally distributed, but with a mean of 64.1 inches and a standard deviation of 2.52 inches. a) If a man is 6 feet 3 inches tall, what is his \( z \)-score (to two decimal places)? \( z= \) b) If a woman is 5 feet 11 inches tall, what is her \( z \)-score (to two decimal places)? \( z= \) c) Who is relatively taller? The 6 foot 3 inch American man The 5 foot 11 inch American woman

To find the \( z \)-score for the man who is 6 feet 3 inches tall (which is 75 inches), use the formula \( z = \frac{(X - \mu)}{\sigma} \). Plugging in the values gives \( z = \frac{(75 - 69.2)}{2.64} \approx 2.20 \). For the woman who is 5 feet 11 inches tall (which is 71 inches), the formula gives \( z = \frac{(71 - 64.1)}{2.52} \approx 2.75 \). In terms of relative height, the woman has a higher \( z \)-score, meaning she is relatively taller compared to her gender's average! A fun fact: The term "normal distribution" might evoke thoughts of conformity, but it actually relates to many intriguing phenomena in nature and social sciences. These distributions help explain everything from human heights to the spread of certain traits in populations! Ever wondered how this all plays out in the real world? Height statistics can affect fashion, sports, and even advertising. Brands often tailor their marketing approaches based on average heights and their variations, ensuring they resonate with their audience—making a tall guy or gal feel right at home!