heights of women have a bell-shaped distribution with a mean of 160 cm and a sta

Question

heights of women have a bell-shaped distribution with a mean of 160 cm and a standard deviation of 5cm. using chebyshev’s theorem, what do you know about the percentage of women with heights that are within 3 standard deviations of the mean? what the minimum and maximum heights that are within 3 standard deviations of the mean heights of women have a bell-shaped distribution with a mean of 160 cm and a standard deviation of 5cm. using chebyshev’s theorem, what do you know about the percentage of women with heights that are within 3 standard deviations of the mean? what the minimum and maximum heights that are within 3 standard deviations of the mean heights of women have a bell-shaped distribution with a mean of 160 cm and a standard deviation of 5cm. using chebyshev’s theorem, what do you know about the percentage of women with heights that are within 3 standard deviations of the mean? what the minimum and maximum heights that are within 3 standard deviations of the mean

Explanation / Answer

As per the Chebychev's theorem, (1 - 1/k^2) proportion of data lies between k standard deviation from the mean.

Hence,

Percentage of heights lie within 3 SD from mean = (1 - 1/9) = 8/9 = Atleast 88.89%

Minimum height = 160 - 3*5 = 145

Maximum height = 160 + 3*5 = 175

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