6. Eight tasks were given to each of 125 randomly selected job applicants. The number of tasks failed by each applicant is recorded.
The results are as follows
| Number of tasks failed by an applicant | 0 | 1 | 2 | 3 | 4 | 5 | 6 or more |
| Frequency | 2 | 21 | 45 | 42 | 12 | 3 | 0 |
- Show that the probability of a randomly selected task, from this sample, being failed is 0.3
An employer believes that a binomial distribution might provide a good model for the number of tasks, out of 8, that an applicant fails.
He uses a binomial distribution, with the estimated probability 0.3 of a task being failed. The calculated expected frequencies are as follows
| Number of tasks failed by an applicant | 0 | 1 | 2 | 3 | 4 | 5 | 6 or more |
| Expected frequency | 7.21 | 24.71 | 37.06 | \(r\) | 17.02 | 5.83 | \(s\) |
- Find the value of \(r\) and the value of \(s\) giving your answers to 2 decimal places.
- Test, at the \(5 \%\) level of significance, whether or not a binomial distribution is a suitable model for these data. State your hypotheses and show your working clearly.
The employer believes that all applicants have the same probability of failing each task.
- Use your result from part(c) to comment on this belief.