A student running for a position in student government believes that 56% of the student body will vote for her. However, she is worried about low voter turnout. Complete parts a through d below. a. Assuming she truly has 56% 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 = 300 students show up for voting. mean = 56, standard deviation = 029 (Round to three decimal places as needed.) b. Is it reasonable to assume a normal shape for this sampling distribution? Explain. Since there are 168 expected votes for the student and 132 expected votes not for the student, it is reasonable to assume a normal shape (Type integers or decimals. Do not round.) c. How likely is it that she will not get the majority of the vote, that is, a sample proportion of 50% or lower from the 300 votes cast? The probability is 0181 (Round to four decimal places as needed.) d. If instead n = 800 students show up for voting, how likely is it then that she will not win the majority? The probability is (Round to four decimal places as needed.)