would Paul be able to claim that he as in the 100 percentile, if his exam score was based off of extra credit and the highest possible score of the exam was 90% without the extra credit points? What would Paul's ranking be then

First of all, the highest possible score on any test would be 100% of the points.

Need to know Paul's score and the range of scores to say whether he was in the 100th percentile.

To determine Paul's ranking, we need more information about the scores obtained by other students in the class. The 100th percentile represents the highest rank in a given dataset, meaning that no one scored higher. However, without knowing the scores of other students, we cannot determine Paul's ranking with certainty.

However, we can analyze Paul's position relative to the class based on the information you provided. If the highest possible score on the exam without extra credit is 90%, and Paul obtained the maximum score including extra credit, then it is likely that Paul performed exceptionally well. Assuming no other students scored higher than 90%, Paul would likely be in the top percentile of the class.

To determine Paul's precise ranking, you would need to know the scores of other students in the class. Once you have that information, you can compare Paul's score to others and calculate his percentile rank accordingly.