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?

Question

Mathematics

Keira Rosario

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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Madilynn Trevino · Answer 1

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