Heights of women have a bell-shaped distribution with a mean of 158 cm and a sta

Question

Heights of women have a bell-shaped distribution with a mean of 158 cm and a standard deviation of 6 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 of the mean? At least % of women have heights within 3 standard deviations of 158 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

At least 99% of women have heights within 3 standard deviations of 158

158 - 3x6 = 140

158+3x6 = 176

The minimum height that is within 3 standard deviations of the mean is 140 cm

The maximum height that is within 3 standard deviations of the mean is 176 cm

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