Given that 20% of a population has a certain disease, calculate the probability that at least 400 people will have this disease among 1300 people chosen at random from the population.
I tried approximating a Binomial distribution through a Poisson distribution. 1300 * 0,2 = 260.
$$ 1 - \sum_{x = 0}^{399}p(x;260) = 1 - \sum_{x = 0}^{399}\frac{e^{-260} * 260^{x}}{x!} $$
However this number is too far away from reality. Am I using the wrong method here?