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The body temperatures of a group of healthy adults have a​ bell-shaped distribution with a mean of 98.37degreesF and a standard deviation of 0.49degreesF. Using the empirical​ rule, find each approximate percentage below. a. What is the approximate percentage of healthy adults with body temperatures within 2 standard deviations of the​ mean, or between 97.39degreesF and 99.35degrees​F? b. What is the approximate percentage of healthy adults with body temperatures between 97.88degreesF and 98.86degrees​F?

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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

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