9 A school contains 500 students in years 7 to 11 and 250 students in years 12 and 13. A random sample of 20 students is selected to represent the school at a parents' evening. The number of students in the sample who are from years 12 and 13 is denoted by \(X\).
- State a suitable binomial model for \(X\).
Use your model to answer the following.
- Write down an expression for \(\mathrm { P } ( X = x )\).
- State, in set notation, the values of \(x\) for which your expression is valid.
- Find \(\mathrm { P } ( 5 \leqslant X \leqslant 9 )\).
- State one disadvantage of using a random sample in this context.