# 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?

Question
Decimals
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?

2020-11-11
Step 1
Solution
given:
Men: Population mean $$(\mu) = 69.3,$$
Population mean $$(\sigma) = 2.67$$
Women: Population mean $$(\mu) = 64.8,$$
Population mean $$(\sigma) = 2.54$$
formula:
Let "x" be the height of a man.
$$z=\ \frac{x\ -\ \mu}{\sigma}$$
Step 2
Height of a man $$(x) = (6\ \times\ 12)\ +\ 5 = 77$$ inches
$$[\because\ 1\ feet=12\ inches]$$
$$z =\frac{77\ -\69.3}{2.67}$$
$$z = 2.883895131$$
Round to two decimals.
$$z = 2.88$$

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