### Understanding Body Temperature Distributions in Healthy AdultsThe body temperatures of a group of healthy adults are distributed in a bell-shaped (normal) curve, with a mean (average) of 98.15°F and a standard deviation of 0.69°F. Using the empirical rule, we can find the approximate percentages for certain ranges of body temperatures.**Empirical Rule Overview:**The empirical rule states that for a normal distribution:- Approximately 68% of the data falls within 1 standard deviation of the mean.- Approximately 95% of the data falls within 2 standard deviations of the mean.- Approximately 99.7% of the data falls within 3 standard deviations of the mean.#### Questions and Calculations:**a. What is the approximate percentage of healthy adults with body temperatures within 2 standard deviations of the mean, or between 96.77°F and 99.53°F?**This question asks us to use the empirical rule to find the percentage of adults whose body temperatures fall within the range of 2 standard deviations from the mean. #### Calculation:- Mean = 98.15°F- Standard Deviation = 0.69°F- 2 Standard Deviations from the Mean = 2 * 0.69°F = 1.38°F- Range = Mean ± 2 Standard Deviations- Lower Bound = 98.15°F - 1.38°F = 96.77°F- Upper Bound = 98.15°F + 1.38°F = 99.53°FAccording to the empirical rule, **approximately 95%** of healthy adults in this group have body temperatures within 2 standard deviations of the mean.**b. What is the approximate percentage of healthy adults with body temperatures between 97.46°F and 98.84°F?**This question involves finding the percentage of adults whose temperatures fall within a range derived from 1 standard deviation of the mean.#### Calculation:- Mean = 98.15°F- Standard Deviation = 0.69°F- Range for ±1 Standard Deviation: - Lower Bound = 98.15°F - 0.69°F = 97.46°F - Upper Bound = 98.15°F + 0.69°F = 98.84°FAccording to the empirical rule, **approximately 68%** of healthy adults in this

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le, 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 96.77°F and 99.53°F? b. What is the approximate percentage of healthy adults with body temperatures between 97.46°F and 98.84°F? Approximately % of healthy adults in this group have body temperatures within 2 standard deviations of the mean, or between 96.77°F and 99.53°F. ype an integer or a decimal. Do not round.) Approximately % of healthy adults in this group have body temperatures between 97.46°F and 98.84°F. ype an integer or a decimal. Do not round.)

le, 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 96.77°F and 99.53°F? b. What is the approximate percentage of healthy adults with body temperatures between 97.46°F and 98.84°F? Approximately % of healthy adults in this group have body temperatures within 2 standard deviations of the mean, or between 96.77°F and 99.53°F. ype an integer or a decimal. Do not round.) Approximately % of healthy adults in this group have body temperatures between 97.46°F and 98.84°F. ype an integer or a decimal. Do not round.)

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Concept explainers

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The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.

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### Understanding Body Temperature Distributions in Healthy Adults

The body temperatures of a group of healthy adults are distributed in a bell-shaped (normal) curve, with a mean (average) of 98.15°F and a standard deviation of 0.69°F. Using the empirical rule, we can find the approximate percentages for certain ranges of body temperatures.

**Empirical Rule Overview:**
The empirical rule states that for a normal distribution:
- Approximately 68% of the data falls within 1 standard deviation of the mean.
- Approximately 95% of the data falls within 2 standard deviations of the mean.
- Approximately 99.7% of the data falls within 3 standard deviations of the mean.

#### Questions and Calculations:

**a. What is the approximate percentage of healthy adults with body temperatures within 2 standard deviations of the mean, or between 96.77°F and 99.53°F?**

This question asks us to use the empirical rule to find the percentage of adults whose body temperatures fall within the range of 2 standard deviations from the mean.

#### Calculation:
- Mean = 98.15°F
- Standard Deviation = 0.69°F
- 2 Standard Deviations from the Mean = 2 * 0.69°F = 1.38°F
- Range = Mean ± 2 Standard Deviations
- Lower Bound = 98.15°F - 1.38°F = 96.77°F
- Upper Bound = 98.15°F + 1.38°F = 99.53°F

According to the empirical rule, **approximately 95%** of healthy adults in this group have body temperatures within 2 standard deviations of the mean.

**b. What is the approximate percentage of healthy adults with body temperatures between 97.46°F and 98.84°F?**

This question involves finding the percentage of adults whose temperatures fall within a range derived from 1 standard deviation of the mean.

#### Calculation:
- Mean = 98.15°F
- Standard Deviation = 0.69°F
- Range for ±1 Standard Deviation:
- Lower Bound = 98.15°F - 0.69°F = 97.46°F
- Upper Bound = 98.15°F + 0.69°F = 98.84°F

According to the empirical rule, **approximately 68%** of healthy adults in this

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