Problem 8BSC

z Scores. In Exercises, express allz scores with two decimal places.

Student’s Pulse Rate A male student of the author has a measured pulse rate of 52 beats per minute. Based on Data Set 1 in Appendix B, males have a mean pulse rate of 67.3 beats per minute and a standard deviation of 10.3 beats per minute.

a. What is the difference between the student’s pulse rate and the mean pulse rate of males?

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

c. Convert the student’s pulse rate to a z score.

d. If we consider “usual” pulse rates to be those that convert to z scores between −2 and 2, is the student’s pulse rate usual or unusual?

Solution 8BSC

(a)

The difference between the given student’s pulse rate and the mean pulse rateis

Therefore, the student’s pulse rate is15.3 beats per minute below the mean pulse rate.

(b)

We know that, score for a data value found by

.

The score for the given student’s pulse rate is

Therefore, 1.48 standard deviations below the mean pulse rate

(c)

We know that, score for a data value found by

.

The score for the given student’s pulse rate is

Therefore, thescore for the given student’s pulse rate is –1.48.

(d)

The score of the given student’s pulse rate –1.48 lies between –2 and 2. Therefore, the given student’s pulse rate is usual.