3 At a pottery which manufactures mugs, it is known that \(5 \%\) of mugs are faulty. The mugs are produced in batches of 20 . Faults are modelled as occurring randomly and independently. The number of faulty mugs in a batch is denoted by the random variable \(X\).

1. Determine \(\mathrm { P } ( X \geqslant 2 )\).
2. Find \(\operatorname { Var } ( X )\). Independently of the mugs, the pottery also manufactures cups, and it is known that \(7 \%\) of cups are faulty. The cups are produced in batches of 30 . Faults are modelled as occurring randomly and independently. The number of faulty cups in a batch is denoted by the random variable \(Y\).
3. Determine the standard deviation of \(X + Y\). When 10 batches of cups have been produced, a sample of 15 cups is tested to ensure that the handles of the cups are properly attached.
4. Explain why it might not be sensible to select a sample of 15 cups from the same batch.