Hei ts of wormen have a e-haped dsteuson with a mean of 161 am and a standard de

Question

Hei ts of wormen have a e-haped dsteuson with a mean of 161 am and a standard de ation of 8. Using Chebyshev's theorem, what do we know about the percentage of women with he ts 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? Atleast-Nof women have heights within 2 standard deviations of 161 cm. Round to the nearest percent as needed) The minimum height that is within 2 standard deviations of the mean is m The manum hegtthat is whin 2 standard deviators of the mean isCn.

Explanation / Answer

Result:

Chebyshev theorem states that at least 11/k2 of the data lie within k standard deviations of the mean. When k=2, 1-1/22 =3/4 of the value or 75% of the data values falls within 2 standard deviations.

At least 75% of the women have heights within 2 standard deviation of 161 cm.

Minimum height = mean-2*sd = 161-2*8 = 145 cm.

Maximum height = mean+2*sd = 161+*8 =177 cm.

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