Question 747863: Heights of women have a bell-shaped distribution with a mean of 159cm and a standard deviation of 7cm. Using Chebyshev's theorem, what do we know about the percentage of women with heights that are within 3 standard deviations of the mean? What are the minimum and maximum heights that are within 3 standard deviations of the mean?
Answer by FrankM(1040)   (Show Source):
You can put this solution on YOUR website! Chebyshev stated that no more than 1/k2 of the distribution's values can be more than k standard deviations away from the mean.
So 3 standard deviations away means 1/9 of the values fall outside the 3 STD range.
159cm+/-21cm = 148cm min, 180cm max.
The maximum height is 5 ft 11 inches. I can't confirm it's true, but the suggestion that the high end, 1/2 of the outliers, or just 1/18 of the women, are this tall passes the common sense test.
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