A political candidate has hired a polling firm to assess her chances of winning a senatorial election in a large eastern state. She wants an estimate of the proportion of registered voters that would vote for her "if the election were held today." Registered voters are to be randomly chosen, interviewed, and their preferences recorded. The polling firm will use the outcome of \(\bar{X}\) as an estimate of the proportion of voters in favor of the candidate. It is known that currently between 40 percent and 60 percent of the registered voters favor her in the election. She wants to have an estimate that is within 2 percentage points of the true proportion with probability \(=.99\). How many registered voters must be interviewed, based on the asymptotic distribution of \(\bar{X}\) ?