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 n = 589 likely voters (Time, June 26, 2000). Assume the population proportion for a presidential candidate is p = 0.50. The questions below concern the sample proportion of likely voters favoring the presidential candidate.

(a.) What is the probability the Time/CNN poll will provide a sample proportion within plus-or-minus 0.04 of the population proportion?

(b.) What is the probability the Time/CNN poll will provide a sample proportion within plus-or-minus 0.03 of the population proportion?

(c.) What is the probability the Time/CNN poll will provide a sample proportion within plus-or-minus 0.02 of the population proportion?

(d.) Suppose the sample size is increased from n = 589 to n = 1,178. With this new, larger sample size, what is the probability the Time/CNN poll will provide a sample proportion within plus-or-minus 0.02 of the population proportion?