A student running for a position in student government believes that 55% of the student body will vote for her. However, she is worried about low voter turnout.
a. Assuming she truly has 55% support in the entire student body, find the mean and standard deviation of the sampling distribution for the proportion of votes she will receive if only n = 200 students show up for voting.
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 vote, i.e., a sample proportion of 50% or lower from the 200 votes cast?
d. If instead n = 1000 students show up for voting, how likely is it then that she will not win the majority?