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Heights of women have a bell-shaped distribution with a mean of 165 cm and a sta

ID: 3128171 • Letter: H

Question

Heights of women have a bell-shaped distribution with a mean of 165 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 of the mean?

At least ____% of women have heights within 3 standard deviations of 165 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 ____% of women have heights within 3 standard deviations of 165 cm. (Round to the nearest percent as needed.)

When k = 3 standard deviations,

1 - 1/k^2 = 1 - 1/3^2 = 0.8889 = 89% [ANSWER]

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

u - 3*sigma = 165 - 3*7 = 144 [ANSWER]

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

u + 3*sigma = 165 + 3*7 = 186 [ANSWER]

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