I'm a beginner on statistics. And I come up with this question when studying Bernoulli distribution: Let $X_n$ be the sum of $n$ independent trials of a Bernoulli experiment, whose result can be $1$ with probability $p$, and $0$ with probability $1-p$. How to find the minimum $n$, so that $P(X_n>\frac n 2)> 0.95$ ?
Thanks.
ps: after google, I understand the sum of $n$ Bernoulli becomes a binomial distribution. Also the cdf can be calculated for a particular number of $X_n=k$. However it is not clear to me how to solve for $n$ that $P(X_n>\frac n 2)> 0.95$.