3. The number of accidents on a particular stretch of motorway was recorded each day for 200 consecutive days. The results are summarised in the following table.
| Number of accidents | 0 | 1 | 2 | 3 | 4 | 5 |
| Frequency | 47 | 57 | 46 | 35 | 9 | 6 |
- Show that the mean number of accidents per day for these data is 1.6
A motorway supervisor believes that the number of accidents per day on this stretch of motorway can be modelled by a Poisson distribution.
She uses the mean found in part (a) to calculate the expected frequencies for this model. Her results are given in the following table.
| Number of accidents | 0 | 1 | 2 | 3 | 4 | 5 or more |
| Frequency | 40.38 | 64.61 | \(r\) | 27.57 | 11.03 | \(s\) |
- Find the value of \(r\) and the value of \(s\), giving your answers to 2 decimal places.
- Stating your hypotheses clearly, use a \(10 \%\) level of significance to test the motorway supervisor's belief. Show your working clearly.