Most people think that the “normal” adult body temperature is 98.6°F. In a more recent study, researchers reported that a more accurate figure may be 98.1°F. Furthermore, the standard deviation appeared to be around 0.5°F. Assume that a Normal model is appropriate. Complete parts a through c below. a) In what interval would you expect most people’s body temperatures to be? Explain. Select the correct choice below and fill in the answer box(es) to complete your choice. A. Using the 68-95-99.7 Rule, about 95% of the body temperatures are expected to be less than nothing°F. (Round to one decimal place as needed.) B. Using the 68-95-99.7 Rule, about 95% of the body temperatures are expected to be at least nothing°F. (Round to one decimal place as needed.) C. Using the 68-95-99.7 Rule, about 95% of the body temperatures are expected to be between nothing°F and nothing°F. (Use ascending order. Round to one decimal place as needed.)
The Correct Answer and Explanation is:
Correct Answer:
C. Using the 68-95-99.7 Rule, about 95% of the body temperatures are expected to be between 97.1°F and 99.1°F.
Explanation
The commonly held belief that the “normal” adult body temperature is 98.6°F originated from a 19th-century study by Carl Wunderlich. However, more recent research suggests that the average body temperature is closer to 98.1°F, with a standard deviation of 0.5°F. Given this, and assuming body temperatures follow a Normal (Gaussian) distribution, we can use the 68-95-99.7 Rule—also known as the Empirical Rule—to estimate the interval where most body temperatures fall.
According to the 68-95-99.7 Rule:
- Approximately 68% of values lie within 1 standard deviation of the mean.
- About 95% fall within 2 standard deviations.
- Nearly 99.7% lie within 3 standard deviations.
For this problem, we focus on the 95% interval, which corresponds to 2 standard deviations from the mean.
Step-by-step:
- Mean (μ) = 98.1°F
- Standard deviation (σ) = 0.5°F
- 95% interval = μ ± 2σ
So we calculate:
- Lower bound = 98.1 − (2 × 0.5) = 98.1 − 1.0 = 97.1°F
- Upper bound = 98.1 + (2 × 0.5) = 98.1 + 1.0 = 99.1°F
Therefore, we expect about 95% of healthy adult body temperatures to fall between 97.1°F and 99.1°F.
This interval is helpful for clinicians and researchers, as it gives a more accurate understanding of what is “normal” for most people. Body temperatures outside of this range could warrant further investigation, but small deviations may still be physiologically normal depending on the context (e.g., time of day, activity, or individual variability).
