Time/CNN voter polls monitored public opinion for the presidential candidates during the 2000 presidential election campaign. One Time/CNN poll conducted by Yankelovich Partners, Inc., used a sample of 589 likely voters (Time, June 26, 2000). Assume the population proportion for a presidential candidate is p = 0.50. Let P^ be the sample proportion of likely voters favoring the presidential candidate.

(a) Show the sampling distribution of p^

(b) What is the probability the Time/CNN poll will provide a sample result within 4% of the population proportion?

(c) What is the probability the Time/CNN poll will produce a result greater than 54%?