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the heights of adult men in america are normally distributed, with a mean of 69.1 inches and a standard deviation of 2.65 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 2.53 inches.
a) if a man is 6 feet 3 inches tall, what is his z - score (to two decimal places)?
z = 2.22 x

Explanation:

Step1: Convert height to inches

1 foot = 12 inches, so 6 feet 3 inches = 6*12 + 3 = 75 inches.

Step2: Use z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value, $\mu$ is the mean and $\sigma$ is the standard deviation. For men, $\mu = 69.1$ inches and $\sigma=2.65$ inches, and $x = 75$ inches. Then $z=\frac{75 - 69.1}{2.65}$.

Step3: Calculate the z - score

$z=\frac{75 - 69.1}{2.65}=\frac{5.9}{2.65}\approx2.2264\approx2.23$ (rounded to two decimal places).

Answer:

$2.23$