Heights of women have a bell-shaped distribution with a mean of 164 cm and a sta

Question

Heights of women have a bell-shaped distribution with a mean of 164 cm and a standard deviation of 5 cm. Using Chebyshev's theorem, what do we know about the percentage of women with heights that are within 2 standard deviations of the mean? What are the minimum and maximum heights that are within 2 standard deviations of the mean? At least % of women have heights within 2 standard deviations of 164 cm. (Round to the nearest percent as needed.) Enter your answer in the answer box and then click Check Answer.

Explanation / Answer

By Chebyshev's theorem, atleast (1 - 1/k2) data lies between k standard deviations from the mean.

Here,

k = 2

Hence,

Atleast (1 - 1/4) i.e. 75% of the women have heights within 2 SD from the mean.

Mimimum height = 164 - 2*5 = 154

Maximum height = 164 + 2*5 = 174

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