2. If a student is given a detention for not participating in class, then the student is re- quired to spend 30 minutes catching up on work that they have fallen behind on dur- ing the detention. If a student finishes their work early, they must then wait out the rest of the 30 minutes. Assuming that all work is finished by 30 minutes, answer the following. (a) Without any other information on the scenario, what distribution would you use to model the length of time that students spend finishing their work during a detention? Justify your answer. Note: only consider the distributions taught in MXB101. (b) Based on your assumption from part (a), find the expected time taken for the students to finish their work. (c) Based on your assumption from part (a), what is the probability that a student finishes their work within 15 minutes if they haven't finished their work in the first 10 minutes?