Question

The body temperatures of a group of healthy adults have a​ bell-shaped distribution with a mean of 98.15 F and a standard deviation of 51 F. Using the empirical​ rule, find each approximate percentage below.

Answer 1

The application of the Empirical Rule suggests that for a normal distribution of body temperatures, about 68% of data lies within one standard deviation of the mean, 95% within two, and over 99% within three standard deviations.

Step-by-step explanation:

The question involves the concept of the Empirical Rule, which is part of descriptive statistics in mathematics. It pertains to the distribution of body temperatures among healthy adults, which follows a bell-shaped and symmetric distribution. The Empirical Rule states that for such a distribution:

• Approximately 68% of the data falls within one standard deviation of the mean.
• Approximately 95% falls within two standard deviations of the mean.
• More than 99% falls within three standard deviations of the mean.

In the case of body temperature provided, the mean is 98.15°F and the standard deviation is erroneously stated as 51°F (which may be a typo since this is a very large standard deviation for body temperature). Assuming the standard deviation should be a value that makes sense biologically, such as 0.7°F, we would apply the Empirical Rule as described above.