2 An organisation runs courses to train students to become engineers. These students are taught in groups of 8 . The director of the organisation claims that on average \(60 \%\) of the students in a group achieve a pass. A random sample of 150 groups of 8 students is chosen. The following table shows the observed frequencies together with some of the expected frequencies using the appropriate binomial distribution.
| Number of passes per group | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Observed frequency | 0 | 0 | 8 | 24 | 45 | 36 | 26 | 10 | 1 |
| Expected frequency | \(p\) | 1.180 | 6.193 | 18.579 | 34.836 | \(q\) | \(r\) | 13.437 | 2.519 |
- Find the values of \(p , q\) and \(r\) giving your answers correct to 3 decimal places.
- Carry out a goodness of fit test, at the \(10 \%\) significance level, to test whether there is evidence to reject the director's claim.