2013 MJC P2 Q8 [Modified]

1. The random variable \(Y\) has a binomial distribution with mean \(1.6\) and \(\mathrm{P}(Y=0)=0.1296\). Find \(\mathrm{P}(Y>2)\).
2. A car park has a large number of parking lots. \(80\) parking lots are observed and the number of occupied parking lots is denoted by \(X\). State, in context, two assumptions needed for \(X\) to be well modelled by a binomial distribution.

The probability of a parking lot being occupied is \(0.95\). Find the probability that out of the \(80\) chosen parking lots, at least \(90\)% are occupied.