anonymous
  • anonymous
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
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
just the person I was looking for
egbeach
  • egbeach
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egbeach
  • egbeach
what 165+12 and 165-12?

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anonymous
  • anonymous
177 and 153
egbeach
  • egbeach
okay well the women in the wanted range are between those heights
anonymous
  • anonymous
k
egbeach
  • egbeach
we also know that the majority of the women are between those heights
anonymous
  • anonymous
K...so that is my minimum and maximum? what is the percentage of the height within 2 standard deviations of 165?
egbeach
  • egbeach
the percent is 95 and yes that is the min and max
anonymous
  • anonymous
it's not 95% -- you're confusing the empirical rule for Chebyshev's inequality
anonymous
  • 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

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