Final answer:
Steve is faster than Paul as he completes the 100-meter dash in less time. The new stopwatch with ±0.05 s uncertainty is helpful for timing the team's sprints and distinguishes times like 12.04 s from 12.07 s.
Step-by-step explanation:
Comparing their times, Steve is faster than Paul because the time he takes to complete the race is shorter. When discussing the efficiency of a new stopwatch with an uncertainty of ±0.05 seconds, it is determined that this level of uncertainty is acceptable as it will still allow the coach to distinguish between runners with times like 12.04 seconds and 12.07 seconds, which are the times of the first and second-place sprinters. Therefore, the coach's new stopwatch will be helpful in timing the team.
Moreover, when the team's top sprinter clocked a 100-meter sprint at 12.04 seconds one week and then at 11.96 seconds another week, despite the uncertainty of the stopwatch, we can conclude that this week's time was faster. Given that the uncertainty is smaller than the difference in the recorded times, it supports that there was a genuine improvement in speed.