The heights of adult men in America are normally distributed, with a mean of 69.8 inches and a standard deviation of 2.61 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.6 inches and a standard deviation of 2.51 inches. a) If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)

We have been given the heights of adult men in America are normally distributed, with a mean of 69.8 inches and a standard deviation of 2.61 inches. We are asked to find the z-score of height of man with 6 feet 3 inches.

We will use z-score formula to solve our given problem.

[tex]z=\frac{x-\mu}{\sigma}[/tex], where,

z = z-score,

x = Sample score,

[tex]\mu[/tex] = Mean,

[tex]\sigma[/tex] = Standard deviation,

6 feet 3 inches = 72+3 inches = 75 inches

[tex]z=\frac{75-69.8}{2.61}[/tex]

[tex]z=\frac{5.2}{2.61}[/tex]

[tex]z=1.99233716475[/tex]

[tex]z\approx 1.99[/tex]

Therefore, the z-score for the man with height of 6 feet 3 inches is 1.99.