9 The number of visitors arriving at an art exhibition is recorded for each 10 -minute period of time during the ten hours that it is open on a particular day. The results are as follows.
| Number of visitors in a 10 -minute period | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | \(\geqslant 9\) |
| Number of 10 -minute periods | 2 | 2 | 12 | 8 | 11 | 13 | 4 | 7 | 1 | 0 |
- Calculate the mean and variance for this sample and explain whether your answers support a suggestion that a Poisson distribution might be a suitable model for the number of visitors in a 10-minute period.
- Use an appropriate Poisson distribution to find the two expected frequencies missing from the following table.
| Number of visitors in | | a 10-minute period |
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | \(\geqslant 9\) |
| Expected number of | | 10 -minute periods |
| 1.10 | | 8.79 | | 11.72 | 9.38 | 6.25 | 3.57 | 1.79 | 1.28 |
- Test, at the \(10 \%\) significance level, the goodness of fit of this Poisson distribution to the data.