Posted by **LISA** on Sunday, February 13, 2011 at 1:33pm.

It is well known that the heights of individual American men are normally distributed with mean 70 inches and standard deviation 2.8 inches.

The Central Limit Theorem states that if n men are randomly chosen, then their average height will also be normally distributed with mean 70 inches (so the mean is unchanged), but the standard deviation will not be 2.8 inches--it will be 2.8 divided by the square root of n (the standard deviation is smaller for groups than for individuals). This means that there is less variation among group averages than there is between individuals--I hope that makes intuitive sense.

a) How likely is it that a randomly chosen man would be more than six feet tall (i.e., what percentage of men are over six feet)?

b) How likely is it that a randomly chosen group of ten men would have an average height exceeding six feet?

Remember: The answer is never sufficient:

What's of interest is always the explanation!

## Answer this Question

## Related Questions

- stat - assume that the heights of men are normally distributed with a mean of 68...
- statistics - The heights of South African men are normally distributed with a ...
- Statistics - In a murder trial in Los Angeles, a shoe expert stated that the ...
- statistics - Suppose that the heights of adult men in the United States are ...
- statistics - Suppose that the heights of adult men in the United States are ...
- statistics - The distribution of heights of American women aged 18 to 24 is ...
- Statistics - The distribution of heights of American women aged 18 to 24 is ...
- Statistics - The Boeing 757-200 ER airliner carries 200 passengers and has doors...
- Statistics - The heights of 18-year-old men are approximately normally ...
- statistics - The distribution of the heights of men in the U.S. is normally ...