6. An airport manager carries out a survey of families and their luggage. Each family is allowed to check in a maximum of 4 suitcases. She observes 50 families at the check-in desk and counts the total number of suitcases each family checks in. The data are summarised in the table below.
| Number of suitcases | 0 | 1 | 2 | 3 | 4 |
| Frequency | 6 | 25 | 12 | 6 | 1 |
The manager claims that the data can be modelled by a binomial distribution with \(p = 0.3\)
- Test the manager's claim at the \(5 \%\) level of significance. State your hypotheses clearly.
Show your working clearly and give your expected frequencies to 2 decimal places.
(8)
The manager also carries out a survey of the time taken by passengers to check in. She records the number of passengers that check in during each of 100 five-minute intervals.
The manager makes a new claim that these data can be modelled by a Poisson distribution. She calculates the expected frequencies given in the table below.
| Number of passengers | 0 | 1 | 2 | 3 | 4 | 5 or more |
| Observed frequency | 5 | 40 | 31 | 18 | 6 | 0 |
| Expected frequency | 16.53 | 29.75 | \(r\) | \(s\) | 7.23 | 3.64 |
- Find the value of \(r\) and the value of \(s\) giving your answers to 2 decimal places.
- Stating your hypotheses clearly, use a \(1 \%\) level of significance to test the manager's new claim.