According to a random sample taken at 12 A. M., body temperatures of healthy adults have a bell-shaped distribution with a mean of 98.28degreesF and a standard deviation of 0.63degreesF. 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? At least nothing % of healthy adults have body temperatures within 2 standard deviations of 98.28degreesF.

Question

Mathematics

Lailah Garcia

21 September, 08:35

According to a random sample taken at 12 A. M., body temperatures of healthy adults have a bell-shaped distribution with a mean of 98.28degreesF and a standard deviation of 0.63degreesF. 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? At least nothing % of healthy adults have body temperatures within 2 standard deviations of 98.28degreesF.

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Davila · Answer 1

At least 75% of healthy adults have body temperatures within 2 standard deviations of 98.28degreesF.

The minimum possible body temperature that is within 2 standard deviation of the mean is 97.02F and the maximum possible body temperature that is within 2 standard deviations of the mean is 99.54F.

Step-by-step explanation:

Chebyshev's theorem states that, for a normally distributed (bell-shaped) variable:

75% of the measures are within 2 standard deviations of the mean

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 within 2 standard deviations of 98.28degreesF.

Range:

Mean: 98.28

Standard deviation: 0.63

Minimum = 98.28 - 2*0.63 = 97.02F

Maximum = 98.28 + 2*0.63 = 99.54F

The minimum possible body temperature that is within 2 standard deviation of the mean is 97.02F and the maximum possible body temperature that is within 2 standard deviations of the mean is 99.54F.