5. A traffic analyst is interested in the number of heavy lorries passing a certain junction. He counts the numbers of lorries in 100 five-minute intervals, and gets the following results:
| Number of lorries in | | five-minute interval, \(X\) |
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Number of intervals | 7 | 13 | 25 | 19 | 15 | 10 | 7 | 4 |
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\section*{STATISTICS 2 (A) TEST PAPER 9 Page 2}
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- Show that the mean of \(X\) is 3 , and find the variance of \(X\).
- Give two reasons for thinking that \(X\) can be modelled by a Poisson distribution. (2 marks)
After a new landfill site has been established nearby, a member of an environmental group notices that 18 lorries pass the junction in a period of 15 minutes. The group claims that this is evidence that the mean number of lorries per five-minute interval has increased. - Test whether the group's claim is valid. Work at the \(5 \%\) significance level, and state your hypotheses clearly.