Binomial and Geometric · Superchallenge problem

A plane has $200$ seats and each ticket holder shows up with probability $0.9$, independently. The airline sells $n$ tickets and wants $P(\text{more than } 200 \text{ show up}) \le 0.05$. Using the normal approximation with continuity correction and $z = 1.645$, what is the largest $n$ it can sell?