Question

In Exercises 5–8, express all z scores with two decimal places.

Female Pulse Rates Pulse rates of adult females are listed in Data Set 1 “Body Data” in Appendix B. The lowest pulse rate is 36 beats per minute, the mean of the listed pulse rates is x = 74.0 beats per minute, and their standard deviation is s = 12.5 beats per minute.

a. What is the difference between the pulse rate of 36 beats per minute and the mean pulse rate of the females?

b. How many standard deviations is that [the difference found in part (a)]?

c. Convert the pulse rate of 36 beats per minutes to a z score.

d. If we consider pulse rates that convert to z scores between -2 and 2 to be neither significantly low nor significantly high, is the pulse rate of 36 beats per minute significant?

Short answer

a. The difference between the given pulse rate of 36 beats per minute and the mean pulse rate is equal to -38 beats per minute.

b. The difference between the given pulse rate of 36 beats per minute and the mean pulse rate is 3.04 standard deviations.

c. -3.04 is the z-score value for the given pulse rate.

d. The pulse rate equal to 36 beats per minute is significantly low.

Step-by-step solution

Given information

The pulse rates of females are tabulated.

The mean female pulse rate is given as 74.0 beats per minute.

The standard deviation of the female pulse rate is given as 12.5 beats per minute.

The formula of z-score

The following is the expression of thez-score for a given data value (x):

$z=\frac{x-\overline{x}}{s}$

Here,$\overline{x}$ is the mean of the sample.

s is the standard deviation of the sample.

Calculation

a.

The difference between the pulse rate of 36 beats per minute and the mean female pulse rate is computed as shown below:

$$\begin{gathered} x-\overline{x}=36-74 \\ =-38 \end{gathered}$$

Thus, the difference between the pulse rate of 36 beats per minute and the mean female pulse rate is equal to-38 beats per minute.

b.

The difference between the pulse rate of 36 beats per minute and the mean female pulse rateis computed using the z-score as shown below:

$$\begin{gathered} z=\frac{x-\overline{x}}{s} \\ =\frac{36-74}{12.5} \\ =-3.04 \end{gathered}$$

Therefore, the difference is3.04 standard deviations.

c.

The z-score for the given value is computed as shown below:

$$\begin{gathered} z=\frac{x-\overline{x}}{s} \\ =\frac{36-74}{12.5} \\ =-3.04 \end{gathered}$$

Here, the calculated value of the z-score is equal to -3.04.

d.

Since the z-score value is below -2, it can be said that the female pulse rate of 36 beats per minute is significantly low.