Question

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?

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

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