## anonymous one year ago heights of women have a bell shaped distribution with a mean of 165 and a deviation of 6. Using the Cebyshev's theorem, what do we know about the percentage of women with heights that are 2 standard deviations within the mean. what are the minimum and maximum heights that are 2 standard deviations within the mean

1. anonymous

just the person I was looking for

2. egbeach

3. egbeach

what 165+12 and 165-12?

4. anonymous

177 and 153

5. egbeach

okay well the women in the wanted range are between those heights

6. anonymous

k

7. egbeach

we also know that the majority of the women are between those heights

8. anonymous

K...so that is my minimum and maximum? what is the percentage of the height within 2 standard deviations of 165?

9. egbeach

the percent is 95 and yes that is the min and max

10. anonymous

it's not 95% -- you're confusing the empirical rule for Chebyshev's inequality

11. anonymous

https://en.wikipedia.org/wiki/Chebyshev's_inequality#Statement for values at least $$k$$ standard deviations from the mean we have $$P(\frac1\sigma|X-\mu|\ge k)\le \frac1{k^2}$$; so for values at least two standard deviations away, these can comprise at most $$1/4=25\%$$ of the population. so there must be at least $$75%$$ within two standard deviations of the mean