Yoshida Toimi is a candidate for the mayor of a medium-sized Midwestern city. If he receives more than 50% of the votes, he will win the election. Prior to the election, his campaign staff is planning to ask 100 randomly selected voters if they support Yoshida.
a. How many positive responses from this sample of 100 is required so that the probability of 50% or more voters supporting him is 0.95 or more?
b. Carefully state the assumptions required for your answer in part (a).
c. Suppose the campaign is able to ask 400 randomly selected voters. Now what is your answer to the question in part (a)?