Heights of women have a bell-shaped distribution with a mean of 162 cm and a sta

Question

Heights of women have a bell-shaped distribution with a mean of 162 cm and a standard deviation of 7 cm. 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 o f the mean? At least % of women have heights within 3 standard deviations of 162 cm. (Round to the nearest percent as needed.) The minimum height that is within 3 standard deviations of the mean is cm. The maximum height that is within 3 standard deviations of the mean is cm.

Explanation / Answer

Byu Chebyshev's theorem, at least 1-1/k^2 lie within k standard deviations.

Thus, 1 - 1/3^2 = 0.888889 = 89% (at least) lie within 3 standard deviations. [ANSWER, 89%]

*******************

As

u = 162
sigma = 7 cm

Then

minimum = 162 - 3*7 = 141
maximum = 162 + 3*7 = 183 [ANSWERS]

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