Planetarium reservation limit under a risk constraint

The Horizon Planetarium has \(96\) seats for each evening show. To reduce the number of empty seats, it accepts more reservations than the number of seats available. Past records show that a reservation holder attends the show with probability \(0.88\). For a particular evening show, \(106\) reservations have been accepted. Let \(X\) denote the number of reservation holders who attend.

1. State two assumptions needed for \(X\) to be well modelled by a binomial distribution.[2]
2. Assume that the assumptions in part (a) hold. Find the probability that there are insufficient seats for the show.[2]
3. Determine the maximum number of reservations that the planetarium may accept so that the probability of having insufficient seats is less than \(2\%\).[3]