A professor is studying the performance of various student groups in his class. Let the random variable X represent a students final score in the class and define the following conditioning events
- F = {student is a freshman}
- So = {student is a sophomore}
- J = {student is a junior}
- Se = {student is a senior}
- M = {student is a male}
- F = {student is a female}
(a) Suppose the average score among males is E[X|M]= 73.2 and the average score among females is E[X|F] = 75.8 . If the overall class average score is E [X| F] = 74.6 , what percentage of the class is female?