Final answer:
To be in the fastest 3% of his laps, Mr. Wilcox needs a laptime that is faster than 97% of his laps, placing him at or below the 3rd percentile. In racing, lower percentiles correspond to faster laptimes, which contrasts with other scenarios like exams where a low percentile could also be good as it indicates finishing quickly.
Step-by-step explanation:
To be in the fastest 3% of all his laps, Mr. Wilcox needs a laptime that is faster than 97% of his laps. In percentile terms, this means he needs a laptime at or below the 3rd percentile, since a fast laptime is a lower number.
This aligns with the general idea that a lower percentile in the context of race times indicates a faster performance. For instance, a runner whose time is in the 20th percentile finished faster than 20% of runners, which also means 80% were faster.
Conversely, a bicyclist in the 90th percentile completed the race faster than 90% of the other cyclists, making him among the fastest.
The confusion may arise from interpreting percentiles in different contexts. For example, in academic testing, a low percentile could be considered good, as finishing more quickly on a timed exam is desirable (Solution 2.20). However, in racing, the fastest competitors are those with lower times corresponding to lower percentiles.