# The heights of adult men in America are normally distributed, with a mean of 69.3 inches and a standard deviation of 2.67 inches. The heights of adult

The heights of adult men in America are normally distributed, with a mean of 69.3 inches and a standard deviation of 2.67 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.8 inches and a standard deviation of 2.54 inces.
a) If a man is 6 feet 5 inches tall, what is z-score?
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Step 1
Solution
given:
Men: Population mean $\left(\mu \right)=69.3,$
Population mean $\left(\sigma \right)=2.67$
Women: Population mean $\left(\mu \right)=64.8,$
Population mean $\left(\sigma \right)=2.54$
formula:
Let "x" be the height of a man.

Step 2
Height of a man inches

$z=\frac{77-69.3}{2.67}$
$z=2.883895131$
Round to two decimals.
$z=2.88$