Question: A polling organization polls n = 100 randomly selected registered voters to estimate the proportion of a large population that intends to vote for Candidate Y in an upcoming election. Although it is not known by the polling organization, p = .55 is the actual proportion of the population that prefers Candidate Y.

a. Give the numerical value of the mean of the sampling distribution of p^{^}.

b. Calculate the standard deviation of the sampling distribution of p^{^}.

c. Use the Empirical Rule to find values that fill in the blanks in the following sentence. In about 99.7% of all randomly selected samples of n = 100 from this population, the sample proportion preferring Candidate Y will be between _ _ _ _ _ _ and _ _ _ _ _ _.