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Answer:
The approximate percentage of healthy adults with body temperatures within 2 standard deviations of the mean, or between 97.39°F to 99.35°F is 95%.
The approximate percentage of healthy adults with body temperatures between 97.88°F to 98.86°F is 68%.
Step-by-step explanation:
Mean : [tex]\mu = 98.37[/tex]
Standard deviation : [tex]\sigma = 0.49[/tex]
Empirical rule :
1 ) 68% of the data lies within 1 standard deviation of mean
i.e. 68% of data lies between: [tex]\mu-\sigma[/tex] to [tex]\mu+\sigma[/tex]
So, On the given data
[tex]98.37-0.49[/tex] to [tex]98.37+0.49[/tex]
[tex]97.88[/tex] to [tex]98.86[/tex]
So, 68% of data lies between 97.88°F to 98.86°F.
2) 95% of the data lies within 2 standard deviation of mean
i.e. 95% of data lies between: [tex]\mu-2\sigma[/tex] to [tex]\mu+2\sigma[/tex]
So, On the given data
[tex]98.37-2(0.49)[/tex] to [tex]98.37+2(0.49)[/tex]
[tex]97.39[/tex] to [tex]99.35[/tex]
So, 95% of data lies between 97.39°F to 99.35°F .
3) 99.7% of the data lies within 3 standard deviation of mean
i.e. 99.7% of data lies between: [tex]\mu-3\sigma[/tex] to [tex]\mu+3\sigma[/tex]
So, On the given data
[tex]98.37-3(0.49)[/tex] to [tex]98.37+3(0.49)[/tex]
[tex]96.9[/tex] to [tex]99.84[/tex]
So, 99.7% of data lies between 96.9°F to 99.84°F .
The approximate percentage of healthy adults with body temperatures within 2 standard deviations of the mean, or between 97.39°F to 99.35°F is 95%.
The approximate percentage of healthy adults with body temperatures between 97.88°F to 98.86°F is 68%.
The approximate percentage of healthy adults with body temperatures within 2 standard deviations of the mean, or between 97.39°F to 99.35°F is 95%.
The approximate percentage of healthy adults with body temperatures between 97.88°F to 98.86°F is 68%.
Given that,
The body temperatures of a group of healthy adults have a bell-shaped distribution with a mean of 98.37degreesF,
Standard deviation of 0.49degreesF.
We have to find,
Using the empirical rule, find each approximate percentage below. the approximate percentage of healthy adults with body.
According to the question,
Mean : [tex]\mu = 98.37[/tex]
Standard deviation : [tex]\sigma = 0.49[/tex]
By Empirical rule :
- 68% of the data lies within 1 standard deviation of mean,
i.e. 68% of data lies between: [tex]\mu-\sigma[/tex] to [tex]\mu+\sigma[/tex]
So, in the given data,
= 98.37 - 0.49 to 98.37 + 0.49
= 97.88 to 98.86
So, 68% of data lies between 97.88°F to 98.86°F.
- 95% of the data lies within 2 standard deviation of mean,
i.e. 95% of data lies between: [tex]\mu - 2\sigma[/tex] to [tex]\mu +2\sigma[/tex]
So, in the given data,
= 98.37 - 2(0.49) to 98.37 + 2(0.49)
= 97.39 to 99.35
So, 95% of data lies between 97.39°F to 99.35°F .
- 99.7% of the data lies within 3 standard deviation of mean,
i.e. 99.7% of data lies between:
So, in the given data,
[tex]\mu-3\sigma[/tex] to [tex]\mu+3\sigma[/tex]
= 98.37 - 3(0.49) to 98.37 + 3(0.49)
So, 99.7% of data lies between 96.9°F to 99.84°F .
The approximate percentage of healthy adults with body temperatures within 2 standard deviations of the mean, or between 97.39°F to 99.35°F is 95%.
The approximate percentage of healthy adults with body temperatures between 97.88°F to 98.86°F is 68%.
For more information about Standard deviation click the link given below.
https://brainly.com/question/23044118
