Heights of women have a bell-shaped distribution with a mean of 161cm and a stan

Question

Heights of women have a bell-shaped distribution with a mean of 161cm and a standard deviation of 5cm. 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 161 cm. (Round to the nearest percent as needed.)

The minimum height that is within 2 deviations of the mean is_____ cm.

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

Explanation / Answer

a)

Using Chebyshev's theorem, what do we know about the percentage of women with heights that are within 2 standard deviations of the mean?

As k = 2, then at least

1 - 1/k^2 = 1 - 1/2^2 = 0.75 = 75% [ANSWER]

of women have heights within 2 standard deviations of 161 cm. [ANSWER, 75%]

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b)

What are the minimum and maximum heights that are within 2 standard deviations of the mean?

Minimum = u - 2*sigma = 161 - 2*5 = 151 [ANSWER]
Maximum = u + 2*sigma = 161 + 2*5 = 171 [ANSWER]

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