4 On average, 1 in 400 microchips made at a certain factory are faulty. The number of faulty microchips in a random sample of 1000 is denoted by \(X\).
- State the distribution of \(X\), giving the values of any parameters.
- State an approximating distribution for \(X\), giving the values of any parameters.
- Use this approximating distribution to find each of the following.
- \(\mathrm { P } ( X = 4 )\).
- \(\mathrm { P } ( 2 \leqslant X \leqslant 4 )\).
- Use a suitable approximating distribution to find the probability that, in a random sample of 700 microchips, there will be at least 1 faulty one.