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 Males Based on Data Set 1 “Body Data” in Appendix B, males have pulse rates with a mean of 69.6 beats per minute and a standard deviation of 11.3 beats per minute. Is a pulse rate of 50 beats per minute significantly low or significantly high? (All of these pulse rates are measured at rest.) Explain.

Short answer

The significant values are separated using limits equal to(47.0 beats per minute, 92.2 beats per minute).

The value equal to 50 beats per minute is not significant.

Step-by-step solution

Given information

The mean male pulse rate is equal to 69.6 beats per minute.

The standard deviation of the male pulse rate is equal to 11.3 beats per minute.

Identifying the limits 

The given set of rules are used to compute the limits that separate the significant valuespresent in a dataset. Here, the mean is denoted by $\mu$, and the standard deviation is denoted by $\sigma$.

Upper limit:$\mu +2\sigma$

Lower limit: $\mu -2\sigma$

The values equal to and above the upper limit are significantly high.

The values equal to and below the lower limit are significantly low.

The values in the interval of the limits are not significant.

The following are the calculations involved to compute the limits:

Lower limit:

$$\begin{gathered} \mu -2\sigma =69.6-2\times 11.3 \\ =69.6-22.6 \\ =47.0 \end{gathered}$$

.

Upper limit:

$$\begin{gathered} \mu +2\sigma =69.6+2\times 11.3 \\ =69.6+22.6 \\ =92.2 \end{gathered}$$

Therefore, the limits are equal to (47.0 beats per minute, 92.2 beats per minute).

Checking for significance

Since the value equal to 50 beats per minute lies in the interval of the limits (47.0,92.2), the value is not significant.