7.14 Beauty contest election A finalist of a Miss University contest believes that 52% of Facebook voters will vote for her. However, she is worried about low voter turnout.

a. Assuming she truly has the support of 52% of all Facebook voters, find the mean and standard deviation of the sampling distribution for the proportion of the votes she will receive if only n = 400 Facebook users were to vote willingly in this competition.

b. Is it reasonable to assume a normal shape for this sampling distribution? Explain.

c. How likely is it that she will not get the majority of the votes, i.e., a sample proportion of 50% or lower from the 400 votes cast?

d. If instead n = 2000 Facebook users are voting in the competition, then how likely is it that she will not win the majority of the votes?