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Question

Heights of women have a bell-shaped distribution with a mean of 164 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 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.)

The minimum height that is within 2 standard deviations of the mean is ? cm.
The maximum height that is within 2 standard deviations of the mean is ? cm.

Answer 1

Marie,

 

Chebyshev's theorem says that at least 75% of all women have a height within two standard deviations of the mean. This means at least 75% of women are between the height 164-2*6=152cm and 164+2*6=176cm tall.

 

Hope that helps!