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21 May, 06:38

According to a random sample taken at 12 A. M., body temperatures of healthy adults have a bell-shaped distribution with a mean of 98.12degreesF and a standard deviation of 0.58degreesF. Using Chebyshev's theorem, what do we know about the percentage of healthy adults with body temperatures that are within 2 standard deviations of the mean? What are the minimum and maximum possible body temperatures that are within 2 standard deviations of the mean?

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  1. 21 May, 07:49
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    At least 75% of healthy adults have body temperatures that are within 2 standard deviations of the mean.

    Minimum: 98.12 - 2*0.58 = 96.96ºF

    Maximum: 98.12 + 2*0.58 = 99.28ºF

    Step-by-step explanation:

    Chebyshev's theorem states that:

    At least 75% of the measures are within 2 standard deviations of the mean.

    At least 89% of the measures are within 3 standard deviations of the mean.

    Using Chebyshev's theorem, what do we know about the percentage of healthy adults with body temperatures that are within 2 standard deviations of the mean?

    At least 75% of healthy adults have body temperatures that are within 2 standard deviations of the mean.

    What are the minimum and maximum possible body temperatures that are within 2 standard deviations of the mean?

    Mean = 98.12

    Standard deviation = 0.58

    Minimum: 98.12 - 2*0.58 = 96.96ºF

    Maximum: 98.12 + 2*0.58 = 99.28ºF
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