Calculate variance of linear transformation

A question is this type if and only if it asks to find Var(aX+b) for a binomial random variable X.

1 questions

CAIE S2 2021 June Q2
2 The random variable \(X\) has the distribution \(\mathrm { B } ( 400,0.01 )\).
  1. Find \(\operatorname { Var } ( 4 X + 2 )\).
    1. State an appropriate approximating distribution for \(X\), giving the values of any parameters. Justify your choice of approximating distribution.
    2. Use your approximating distribution to find \(\mathrm { P } ( 2 \leqslant X \leqslant 5 )\).