We are missing some important context about the problem, and thus aren't in a position to firmly understand what the TS means when he says that the 3.9% figure is "the exact" solution. He could mean nothing more than that it is the solution that was provided, with no actual claim that it is somehow exact. If it were truly meant to reflect an "exact" solution, I would expect at least one more sig fig to be given. We also don't know how detailed of an analysis was expected and what factors were to be considered and what was to be ignored. Does the fact that specific diode type was given mean that part of the exercise was to consider things like the actual (typical) forward diode drop during the brief time that they are conducting a rather substantial current? It would help if the TS would show some work, but that doesn't appear likely to happen.
Doing the normal, simplified analysis I get a ripple of 3.79% if I define the ripple as the voltage droop divided by the peak voltage. If, instead, I define the ripple as the voltage droop divided by the average voltage I get 3.86%, which rounds to the given answer. I would expect that if I divide by the rms voltage I would get a slightly smaller, but very close, value.
Doing the normal, simplified analysis I get a ripple of 3.79% if I define the ripple as the voltage droop divided by the peak voltage. If, instead, I define the ripple as the voltage droop divided by the average voltage I get 3.86%, which rounds to the given answer. I would expect that if I divide by the rms voltage I would get a slightly smaller, but very close, value.