Question

In Exercises 33–36, use the range rule of thumb to identify the limits separating values that are significantly low or significantly high

Body Temperatures Based on Data Set 3 “Body Temperatures” in Appendix B, body temperatures of adults have a mean of 98.20°F and a standard deviation of 0.62°F. (The data from 12 AM on day 2 are used.) Is an adult body temperature of 100oF significantly low or significantly high?

Short answer

The lower limit for body temperatures is given by$96.96{}^{\circ }\text{F}$, and the upper limit is given by$99.44{}^{\circ }\text{F}$.

The adult body temperature of 100${}^{\circ }\text{F}$ is significantly high.

Step-by-step solution

Given information

A set of 107 body temperatures of adults are recorded in degrees Fahrenheit.

The mean adult temperature is equal to 98.20${}^{\circ }\text{F}$.

The standard deviation of the adult temperature is equal to 0.62${}^{\circ }\text{F}$

Identifying the limits 

Considering the mean value $\mu$and the standard deviation $\sigma$, the following are the three conventions under the range rule of thumb that are applied to distinguish significant values.

• Observations equal to and beyond $\mu +2\sigma$ are significantly high.
• Observations equal to and lower than$\mu -2\sigma$ are significantly low.
• Between these two limits lie all the insignificant observations.

The calculations are done as follows:

Lower limit:

$$\begin{gathered} \mu -2\sigma =98.20-2\times 0.62 \\ =98.20-1.24 \\ =96.96 \end{gathered}$$

.

Upper limit:

$$\begin{gathered} \mu +2\sigma =98.20+2\times 0.62 \\ =98.20+1.24 \\ =99.44 \end{gathered}$$

Therefore, the limits are obtained as $\left(96.96{}^{\circ }F,99.44{}^{\circ }F\right)$.

Checking for significance

As the value of the adult body temperature equal to 100${}^{\circ }\text{F}$is beyond the upper limit of 99.44${}^{\circ }\text{F}$, the value of 100${}^{\circ }\text{F}$issignificantly high.