Question

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

Pulse Rates of Females Based on Data Set 1 “Body Data” in Appendix B, females have pulse rates with a mean of 74.0 beats per minute and a standard deviation of 12.5 beats per minute. Is a pulse rate of 44 beats per minute significantly low or significantly high? (All of these pulse rates are measured at rest.)

Short answer

The limits separating significant values are (49.0 beats per minute,99.0 beats per minute).

The value equal to 44 beats per minute is significantly low.

Step-by-step solution

Given information

The mean female pulse rate is equal to 74.0 beats per minute.

The standard deviation of the female pulse rate is equal to 12.5 beats per minute.

Identifying the limits 

The significant valuesusing the range rule of thumb are identified with the following rule:

• The values that are equal to or less than $\mu -2\sigma$ are significantly low.
• The values that are equal to or greater than $\mu +2\sigma$are significantly high.
• The values that lie between$\mu -2\sigma$ and $\mu +2\sigma$ are not significant.

Here, is the mean of the data andis the standard deviation of the data.

Substituting the values, you get:

Lower limit:

.$$\begin{gathered} \mu -2\sigma =74.0-2\times 12.5 \\ =74.0-25.0 \\ =49.0 \end{gathered}$$

Upper limit:

$$\begin{gathered} \mu +2\sigma =74.0+2\times 12.5 \\ =74.0+25.0 \\ =99.0 \end{gathered}$$

.

Therefore, the limits become (49.0 beats per minute, 99.0 beats per minute).

Checking for significance

All values below 49.0 and above 99.0 are considered to be significant.

Since the value equal to 44.0 beats per minute lies below the lower limit of 49.0 beats per minute, it is a significantly low value.