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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.)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 26PFA
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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
Transcribed Image Text:### 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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