The heights of women aged 20 to 29 follow approximately the N (64, 4) distribution. Men the same age have heights distributed as N (69.8, 1.1).

What percent of young women are taller than the mean height of young men?

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28

for real i think its 7.4 but im not sure

To find the percentage of young women who are taller than the mean height of young men, we need to compare the distribution of heights for women and men and find the corresponding percentile.

1. Calculate the z-score for the mean height of young men:
The z-score formula is: z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.
For young men, the mean height is 69.8 and the standard deviation is 1.1. Let's calculate the z-score:
z = (69.8 - 69.8) / 1.1 = 0
The z-score for the mean height of young men is 0.

2. Determine the percentile for the z-score found in step 1:
We can use a standard normal distribution table (Z-table) or a statistical calculator to find the percentile.
The percentile corresponding to a z-score of 0 is 50%, as it represents the mean.

3. Find the percentage of young women
Since the heights of young women follow the N(64, 4) distribution, we want to find the percentage of women taller than the mean height of young men (which is 69.8 in this case).
Calculate the z-score for 69.8 using the same formula as in step 1:
z = (69.8 - 64) / 4 = 1.45
The z-score for a height of 69.8 is approximately 1.45.

Using the Z-table or a statistical calculator, find the percentile corresponding to a z-score of 1.45. Let's assume it is P.
The percentage of young women taller than the mean height of young men is:
100% - P%

Note: The exact percentage will depend on the precision of the z-table or statistical calculator used.