Sophie, 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 π, the proportion of students who support the president. She decides her prior mean is .5, and her prior standard deviation is .15.

(a) Determine the beta

(a,

b) prior that matches her prior belief.

(b) What is the equivalent sample size of her prior?

(c) Out of the 68 students that she polls, y = 21 support the current president.
Determine her posterior distribution.