5. A child is playing with a set of red and blue wooden cubes. The side length of the red cubes is normally distributed with a mean of 14.5 cm and a variance of \(16.0 \mathrm {~cm} ^ { 2 }\). The side length of the blue cubes is normally distributed with a mean of 12.2 cm and a variance of \(9.0 \mathrm {~cm} ^ { 2 }\).

1. Find the probability that a randomly chosen red cube will have a side length of more than 3 cm greater than a randomly chosen blue cube. The child makes two towers, one from 4 red cubes and one from 5 blue cubes. Assuming that the cubes for each colour of tower were chosen at random,
2. find the probability that the red tower is taller than the blue tower.
3. Explain why the assumption that the cubes for each tower were chosen at random is unlikely to be realistic.