Questions: The heights of adult men in America are normally distributed, with a mean of 69.8 inches and a standard deviation of 2.63 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.3 inches and a standard deviation of 2.56 inches. a. If a man is 6 feet 3 inches tall, what is his z-score (to 4 decimal places)? z= b. If a woman is 5 feet 11 inches tall, what is her z-score (to 4 decimal places)? z= c. Who is relatively taller? The 6 foot 3 inch American man The 5 foot 11 inch American woman

The $z$-score of the individual's height is 1.977. This means that 97.599% of the population is shorter than the individual, and 2.401% is taller.

To calculate the $z$-score, we use the formula $z = \frac{X - \mu}{\sigma}$, where $X$ is the individual's height, $\mu$ is the mean height of the population, and $\sigma$ is the standard deviation of the population's height. Substituting the given values, we get $z = \frac{71 - 64.3}{2.56} = 2.617$.

A $z$-score of 2.617 indicates that the individual is taller than the average. The magnitude of the $z$-score reflects how far and in what direction individuals deviate from the mean.

Using the $z$-score, we find that 99.557% of the population is shorter than the given individual, and 0.443% is taller.

The $z$-score of the individual's height is 2.617. This means that 99.557% of the population is shorter than the individual, and 0.443% is taller.