Exit polling is a popular technique used to determine the outcome of an election prior to results being tallied. Suppose a referendum to increase funding for education is on the ballot in a large town (voting population over 100,000 ). An exit poll of 400 voters finds that 204 voted for the referendum. How likely are the results of your sample if the population proportion of voters in the town in favor of the referendum is 0.49 ? Based on your result, comment on the dangers of using exit polling to call elections: How likely are the results of your sample if the population proportion of voters in the town in favor of the referendum is 0.49 ? The probability that more than 204 people voted for the referendum is (Round to four decimal places as needed.)

Step 1 ：We are given a problem involving exit polling, where we have a sample of 400 voters, 204 of whom voted for a certain referendum. We are asked to find the likelihood of this result if the population proportion of voters in favor of the referendum is 0.49.

Step 2 ：This is a problem of binomial distribution, where we have a number of trials (n=400), a number of successes (x=204), and a probability of success (p=0.49).

Step 3 ：We need to find the probability of getting more than 204 successes. This is equivalent to finding the probability of getting 204 or fewer successes and subtracting that from 1.

Step 4 ：Using the cumulative distribution function (CDF) for a binomial distribution, we find that the probability of getting 204 or fewer successes is approximately 0.8024.

Step 5 ：Subtracting this from 1, we find that the probability of getting more than 204 successes is approximately 0.1976.

Step 6 ：Thus, the final answer is \(\boxed{0.1976}\), which represents the probability that more than 204 people voted for the referendum.