The body temperatures of a group of healthy adults have a bell-shaped distribution with a mean of 98.19degreesF and a standard deviation of 0.61degreesF. Using the empirical rule, find each approximate percentage below. a. What is the approximate percentage of healthy adults with body temperatures within 3 standard deviations of the mean, or between 96.36degreesF and 100.02degreesF? b. What is the approximate percentage of healthy adults with body temperatures between 96.97degreesF and 99.41degreesF?

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dfbustos dfbustos · Answer 1 · 2020-06-20T04:28:30+02:00

Answer:

a) From the empirical rule we know that within 3 deviations from the mean we have 99.7% of the data so then that would be the answer for this case.

b) [tex] z=\frac{96.97-98.19}{0.61}=-2[/tex]

[tex] z=\frac{99.41-98.19}{0.61}=2[/tex]

And within 2 deviations from the mean we have 95% of the values.

Step-by-step explanation:

For this case we know that the distribution of the temperatures have the following parameters:

[tex] \mu = 98.19, \sigma =0.61[/tex]

Part a

From the empirical rule we know that within 3 deviations from the mean we have 99.7% of the data so then that would be the answer for this case.

Part b

We can calculate the number of deviations from the mean with the z score with this formula:

[tex]z=\frac{X -\mu}{\sigma}[/tex]

And using this formula we got:

[tex] z=\frac{96.97-98.19}{0.61}=-2[/tex]

[tex] z=\frac{99.41-98.19}{0.61}=2[/tex]

And within 2 deviations from the mean we have 95% of the values.