A Politician Believes That the Proportion of Voters Who Will $\hat { p }$

Essay

A politician believes that the proportion of voters who will vote for a Coalition candidate in the 2004 general election is 0.65. A sample of 500 voters is selected at random.
a. Assume that the politician is correct and p = 0.65. What is the sampling distribution of the sample proportion $\hat { p }$ ? Explain.
b. Find the expected value and standard deviation of the sample proportion $\hat { p }$ .
c. What is the probability that the number of voters in the sample who will vote for a Labor candidate in the 2004 general election will be between 340 and 350?