Answer to Question #237317 in Statistics and Probability for Leny

Question

What is the approximate percentage of healthy adults with body temperatures within 1 standard deviation of the mean, or between 97.61 and 98.43?

Answer 1

Let $Χ$ be an observation from a normally distributed random variable, $\mu$  be the mean of the distribution, and $σ$ be its standard deviation: $X\sim N(\mu, \sigma).$

Then by the 68–95–99.7 rule

$$P(\mu-1\sigma\leq X\leq \mu+1\sigma)\approx0.6827$$

Thus, 68.27% of healthy adults have body temperatures between 97.41 and 98.43.