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 98.34degreesF and a standard deviation of 0.59degreesF. 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?

Answer 1

There are 89% of healthy adults with body temperatures that are within 3 standard deviations of the​ mean

The minimum value that is within 3 standard deviations of the mean is 96.57.

The maximum value that is within 3 standard deviations of the mean is 100.11.

Explanation:

Chebyshev's theorem states that a minimum of 89% of the values lie within 3 standard deviation of the mean.

So

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?

There are 89% 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?

We have that the mean
`\mu` is 98.34 and the standard deviation
`\sigma` is 0.59. So:

Minimum

`Mi = \mu - 3\sigma = 98.34 - 3(0.59) = 96.57`

Maximum

`Ma = \mu + 3\sigma = 98.34 + 3(0.59) = 100.11`