2 The sides of a fair 12 -sided spinner are labelled \(1,2 , \ldots , 12\).
The spinner is spun and \(X\) is the random variable denoting the number on the side of the spinner that it lands on.
- Suggest a suitable distribution to model \(X\). You should state the value(s) of any parameter(s).
- Find each of the following.
- \(\mathrm { E } ( X )\)
- \(\operatorname { Var } ( X )\)
You are given that \(\mathrm { E } ( X )\) is denoted by \(\mu\) and \(\operatorname { Var } ( X )\) is denoted by \(\sigma ^ { 2 }\). - Determine \(\mathrm { P } \left( \left| \frac { 2 ( X - \mu ) } { \sigma } \right| > 1 \right)\).