Just before a city referendum on a school budget, a local newspaper polls 470 voters in an attempt to predict whether the budget will pass.

Just before a city referendum on a school budget, a local newspaper polls 470 voters in an attempt to predict whether the budget will pass. Suppose that, unknown to everyone, the budget actually has the support of 53% of the voters.

Question. What is the probability the newspaper's sample will lead the newspaper to predict defeat of the referendum, that is, what is the probability that the newspaper's sample results in a sample proportion p̂ less than 0.50 in favor of the referendum?

p̂