According to a random sample taken at 12 A.M., body temperatures of healthy adults have a bell-shaped distribution with a mean of 98.31°F and a standard deviation of 0.66°F. Using Chebyshev's theorem, what do we know about the percentage of healthy adults with body temperatures that are within 3 standard deviations of the mean? What are the minimum and maximum possible body temperatures that are within 3 standard deviations of the mean?

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02-09-2022
Mathematics

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According to a random sample taken at 12 A.M., body temperatures of healthy adults have a bell-shaped distribution with a mean of 98.31°F and a standard deviation of 0.66°F. Using Chebyshev's theorem, what do we know about the percentage of healthy adults with body temperatures that are within 3 standard deviations of the mean? What are the minimum and maximum possible body temperatures that are within 3 standard deviations of the mean?

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varshamittal029 varshamittal029 · Answer 1 · 2022-09-06T19:00:44+02:00

The minimum and maximum possible body temperatures that are within 3 standard deviations of the mean are 96.33 ° F and 100.29 ° F respectively.

By using the Chebychev's theorem, we know that at least 89% of the data values are within 3 standard deviations of the mean.

So, we get that:

Mean - 3 standard deviation = 98.31 ° F - 3 × (0.66 ° F)

= 98.31 ° F - 1.98 ° F

= 96.33 ° F

Mean + 3 standard deviation = 98.31 ° F + 3 × (0.66 ° F)

= 98.31 ° F + 1.98 ° F

= 100.29 ° F

Therefore, the minimum and maximum possible body temperatures that are within 3 standard deviations of the mean are 96.33 ° F and 100.29 ° F respectively.

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