7. A student collects data on the number of bicycles passing outside his house in 5-minute intervals during one morning.
- Suggest, with reasons, a suitable distribution for modelling this situation.
The student's data is shown in the table below.
| Number of bicycles | 0 | 1 | 2 | 3 | 4 | 5 | 6 or more |
| Frequency | 7 | 14 | 10 | 2 | 1 | 2 | 0 |
- Show that the mean and variance of these data are 1.5 and 1.58 (to 3 significant figures) respectively and explain how these values support your answer to part (a).
An environmental organisation declares a "car free day" encouraging the public to leave their cars at home. The student wishes to test whether or not there are more bicycles passing along his road on this day and records 16 bicycles in a half-hour period during the morning.
- Stating your hypotheses clearly, test at the \(5 \%\) level of significance whether or not there are more than 1.5 bicycles passing along his road per 5-minute interval that morning.