Question: A factory makes both rods and copper tubes, with diameters expressed in centimetres. Due to variations in the manufacturing process, it is known that the internal diameter of a copper tube is \(N\left(2.2,0.03^{2}\right)\), while the diameter of a rod is \(N\left(2.15,0.02^{2}\right)\).

- Find the proportion of tubes with an internal diameter less than \(2.14 \mathrm{~cm}\)

- Find the proportion of rods with a diameter greater than \(2.14 \mathrm{~cm}\)

- Find the proportion of rods with a diameter between \(2.16 \mathrm{~cm}\) and \(2.18 \mathrm{~cm}\)

- A rod and tube are chosen at random. Find the probability that the rod will not pass through the tube.

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