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
asked 2020-11-10
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?

Answers (1)

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.
\(z = 2.88\)
0

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