A candidate for office intends to campaign in a state if her initial support level exceeds 30% of the voters. A random sample of 500 voters is taken, and it is decided to campaign if the sample proportion supporting the candidate exceeds 0.275.
a. What is the probability of a decision not to campaign if, in fact, the initial support level is 23%?
b. What is the probability of a decision not to campaign if, in fact, the initial support level is 35%?