4. The number of emergency plumbing calls received per day by a local council was recorded over a period of 80 days. The results are summarised in the table below.
| Number of calls, \(\boldsymbol { x }\) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Frequency | 3 | 13 | 14 | 15 | 10 | 8 | 8 | 6 | 3 |
- Show that the mean number of emergency plumbing calls received per day is 3.5
A council officer suggests that a Poisson distribution can be used to model the number of emergency plumbing calls received per day. He uses the mean from the sample above and calculates the expected frequencies shown in the table below.
| \(\boldsymbol { x }\) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | |
| 2.42 | 8.46 | 14.80 | \(r\) | 15.10 | 10.57 | 6.17 | 3.08 | \(s\) |
- Calculate the value of \(r\) and the value of \(s\), giving your answers correct to 2 decimal places.
- Test, at the \(5 \%\) level of significance, whether or not the Poisson distribution is a suitable model for the number of emergency plumbing calls received per day. State your hypotheses clearly.