3 The length, in centimetres, of a certain type of snake is modelled by the random variable \(X\) with mean 52 and standard deviation 6.1. A random sample of 75 snakes is selected, and the sample mean, \(\bar { X }\), is found.
- Find \(\mathrm { P } ( 51 < \bar { X } < 53 )\).
- Explain why it was necessary to use the Central Limit theorem in the solution to part (i).