Probability that shoe store customer requires shoes of a proper size is $0,15$. Estimate the compass of customer percent among $2000$ visitors of shoe store, which require a proper size, if the compass is need to be guaranteed with a probability $0,98$.
I use De Moivre–Laplace theorem and based on all problem situation I've had: $$P_{2000}\left(\alpha, \beta\right) = 0.98= \Phi\left(\frac{\alpha - 300}{\sqrt{255}}\right)-\Phi\left(\frac{\beta-300}{\sqrt{255}}\right)$$ where $\Phi(x)$ is standard normal distribution.