2 The random variable \(X\) has the distribution \(\mathrm { B } ( 400,0.01 )\).
- Find \(\operatorname { Var } ( 4 X + 2 )\).
- State an appropriate approximating distribution for \(X\), giving the values of any parameters. Justify your choice of approximating distribution.
- Use your approximating distribution to find \(\mathrm { P } ( 2 \leqslant X \leqslant 5 )\).