7 In a certain lottery, 10500 tickets have been sold altogether and each ticket has a probability of 0.0002 of winning a prize. The random variable \(X\) denotes the number of prize-winning tickets that have been sold.
- State, with a justification, an approximating distribution for \(X\).
- Use your approximating distribution to find \(\mathrm { P } ( X < 4 )\).
- Use your approximating distribution to find the conditional probability that \(X < 4\), given that \(X \geqslant 1\).