5 The score on one throw of a 4 -sided die is denoted by the random variable \(X\) with probability distribution as shown in the table.
| \(x\) | 0 | 1 | 2 | 3 |
| \(\mathrm { P } ( X = x )\) | 0.25 | 0.25 | 0.25 | 0.25 |
- Show that \(\operatorname { Var } ( X ) = 1.25\).
The die is thrown 300 times. The score on each throw is noted and the mean, \(\bar { X }\), of the 300 scores is found.
- Use a normal distribution to find \(\mathrm { P } ( \bar { X } < 1.4 )\).
- Justify the use of the normal distribution in part (ii).