Solution:
Step 1 (Evaluate Argument I).
Argument I is weak because it relies on anecdotal evidence. While some successful people may be healthy without regular exercise, this example does not account for other factors affecting health (such as diet, genetics, or lifestyle choices). It does not directly challenge the statement with reliable, generalizable evidence.
Step 2 (Evaluate Argument II).
Argument II is also weak because it makes a generalization about people with busy lifestyles. It assumes they cannot make time for exercise, which is not necessarily true for everyone. Without concrete evidence, this reasoning is insufficient.
Step 3 (Evaluate Argument III).
Argument III is strong because it uses consistent findings from scientific studies to support the statement. Scientific evidence is reliable and directly relevant to proving the benefits of regular exercise for maintaining good health.
Step 4 (Conclusion).
Only Argument III directly supports the statement with credible and strong reasoning.
\[
{\text{Only III is a strong argument (Option (c)}}
\]