Ures of Variation According to a random sample taken at 12 A.M., body temperatures of healthy adults have a bell-shaped distribution with a mean of \( 98.08^{\circ} \mathrm{F} \) and a standard deviation of \( 0.59^{\circ} \mathrm{F} \). Using Chebysher/s do we know about the percentage of healthy adults with body temperatures that are within 2 standard deviations of the mean? What are the minimum and maximum possible body temperatures that standard deviations of the mean? H. \( 9.2 .44,5.17 \) of 11 points At least \( \square \% \) of healthy adults have body temperatures within 2 standard deviations of \( 98.08^{\circ} \mathrm{F} \). (Round to the nearest percent as needed.)

Using **Chebyshev’s Inequality**, we can determine the minimum percentage of healthy adults whose body temperatures lie within a certain number of standard deviations from the mean, regardless of the distribution's shape. Although the distribution is bell-shaped (suggesting a normal distribution), Chebyshev’s Inequality provides a conservative estimate that applies to any distribution. ### Given: - **Mean (μ):** \( 98.08^{\circ} \mathrm{F} \) - **Standard Deviation (σ):** \( 0.59^{\circ} \mathrm{F} \) - **Number of Standard Deviations (k):** 2 ### Chebyshev’s Inequality Formula: \[ \text{At least } 1 - \frac{1}{k^2} \text{ of the data lies within } k \text{ standard deviations of the mean.} \] ### Calculation for \( k = 2 \): \[ 1 - \frac{1}{2^2} = 1 - \frac{1}{4} = \frac{3}{4} = 75\% \] **Therefore:** - **At least 75%** of healthy adults have body temperatures within **2 standard deviations** of the mean. ### Determining the Range: To find the **minimum** and **maximum** body temperatures within 2 standard deviations: \[ \text{Minimum Temperature} = \mu - 2\sigma = 98.08^{\circ} \mathrm{F} - 2(0.59^{\circ} \mathrm{F}) = 96.90^{\circ} \mathrm{F} \] \[ \text{Maximum Temperature} = \mu + 2\sigma = 98.08^{\circ} \mathrm{F} + 2(0.59^{\circ} \mathrm{F}) = 99.26^{\circ} \mathrm{F} \] ### **Summary:** - **At least 75%** of healthy adults have body temperatures between **96.90 °F** and **99.26 °F**.