# The stature of men is normally distributed, with a mean of 69.0 inches and a standard deviation of 2.8 inches. The height of women is normally distributed, with a mean of 63.6 inches and a standard deviation of 2.5 inches. Modeling academy standards require women to be models taller than 66 inches (or 5 feet 6 inches). What percentage of women meet this requirement?

Question
Modeling
The stature of men is normally distributed, with a mean of 69.0 inches and a standard deviation of 2.8 inches. The height of women is normally distributed, with a mean of 63.6 inches and a standard deviation of 2.5 inches. Modeling academy standards require women to be models taller than 66 inches (or 5 feet 6 inches). What percentage of women meet this requirement?

2021-02-12
Step 1 From the given information, the mean of women is 63.6 inches and standard deviation is 2.5 inches. Let X be the height of the women follows normal distribution with $$\mu=63.6\ and\ \sigma=2.5.$$ Modeling academy standards require women to be models taller than 66 inches Step 2 The percentage of women meet this requirement is, Percentage $$=P(X\ >\ 66)^{*}\ 100\%$$
$$=P\left(\frac{X\ -\ \mu}{\sigma}\ >\ (66\ -\ \mu)\sigma\right)^{*}\ 100\%$$
$$=P\left(z\ >\ \frac{66\ -\ 63.6}{2.5}\right)^{*}\ 100\%$$
$$=P(z\ >\ 0.96)^{*}\ 100\%$$
$$=[1\ -\ P(z\ \leq\ 0.96)]^{*}\ 100\%$$
$$=0.1685^{*}\ 100\%$$ from the excel function, $$=1\ −\ NORM.DIST(0.96,\ 0,\ 1,\ TRUE)$$
$$=16.85\%$$

### Relevant Questions

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The distribution of height for a certain population of women is approximately normal with mean 65 inches and standard deviation 3.5 inches. Consider two different random samples taken from the population, one of size 5 and one of size 85.
Which of the following is true about the sampling distributions of the sample mean for the two sample sizes?
Both distributions are approximately normal with mean 65 and standard deviation 3.5.
A
Both distributions are approximately normal. The mean and standard deviation for size 5 are both less than the mean and standard deviation for size 85.
B
Both distributions are approximately normal with the same mean. The standard deviation for size 5 is greater than that for size 85.
C
Only the distribution for size 85 is approximately normal. Both distributions have mean 65 and standard deviation 3.5.
D
Only the distribution for size 85 is approximately normal. The mean and standard deviation for size 5 are both less than the mean and standard deviation for size 85.
E