Binomial and Geometric · Superchallenge problem

A fair coin is tossed $n$ times, $n$ even, and $X$ is the number of heads. With a continuity correction, $P(X = n/2)$ is approximated by the normal area over an interval of width $1$ centred at the mean, which is about $\dfrac{1}{\sigma\sqrt{2\pi}}$ (the height of the normal curve at its peak), where $\sigma$ is the SD of $X$. Using this approximation, what is the smallest even $n$ for which $P(X = n/2) < 0.05$?