6.2k views
0 votes
A medical researcher who is examining patients as part of a study on heart disease conducts an experiment on a group of males involving jogging on a treadmill and recording the number of minutes that the subject could maintain a fixed speed. The researcher summarized his experiment statistically as follows:

Weight of subject (pounds): Ave. = 180, SD = 24.

Time on treadmill (minutes): Ave. = 40, SD = 10, r = −0.6.

(a) Approximately what percentage of males who weigh 192 pounds can be expected to jog longer than 49 minutes

on the treadmill?

1 Answer

5 votes

Final answer:

Approximately 30.85% of males who weigh 192 pounds or more can be expected to jog longer than 49 minutes on the treadmill.

Step-by-step explanation:

To answer this question, we need to use the information provided about the average weight and time on the treadmill of the male subjects. The mean weight of the subjects is 180 pounds, with a standard deviation of 24 pounds. The mean time on the treadmill is 40 minutes, with a standard deviation of 10 minutes. We also have a correlation coefficient of -0.6 between weight and treadmill time.

We can use the mean and standard deviation information to determine the Z-score for a weight of 192 pounds. The Z-score formula is Z = (X - mean) / standard deviation. Substituting the values, we have Z = (192 - 180) / 24 = 0.5. The Z-score represents the number of standard deviations above or below the mean a particular value is. Using a Z-table or calculator, we can find that a Z-score of 0.5 corresponds to a percentage of approximately 69.15%.

To find the percentage of males who weigh 192 pounds and can be expected to jog longer than 49 minutes, we can use the correlation coefficient. Since the correlation coefficient is negative (-0.6), we expect that as weight increases, the time on the treadmill decreases. So, a weight of 192 pounds, which is above the mean weight, would correspond to a Z-score greater than 0.5. Similarly, a time on the treadmill of 49 minutes would correspond to a Z-score greater than 0. Using the same Z-table or calculator, we can find the percentage of values greater than a Z-score of 0.5, which is approximately 30.85%. Therefore, approximately 30.85% of males who weigh 192 pounds or more can be expected to jog longer than 49 minutes on the treadmill.

User Deion
by
7.7k points