S-ophie, the editor of the student newspaper, is going to conduct a survey of students to determine the level of support for the current president of the students' association. She needs to determine her prior distribution for p, the proportion of students who support the president. She decides her prior mean is 0.5, and her prior standard deviation is {1.15. {a} Determine the barium, h) prior that matches her prior helief. {I5 marks} (b) lOut of the 68 students that she polls, 21 support the current president. Determine her posterior distribution. {4 marks}