I am asking to use central limit theorem to solve this quesion.
In an election between two candidates, A and B, one million individuals cast their vote. Among these, 2000 know candidate A from her election campaign and vote unanimously for her. The remaining 998000 voters are undecided and make their decision independently of each other by flipping a fair coin. Approximate the probability pA that candidate A wins up to 3 significant figures.
I got my mean = np = (1000000-2000) * 0.5 = 499000, my sd =$\sqrt {np*(1-p)}$= $\sqrt {998000*0.5*(1-0.5)}$, then apply CLT, my new sd = $\frac{sd}{\sqrt{998000}}$, and X = $\frac{1000000}{2}$+1-2000 = 498001. Then apply normal distribution. Am I right?