7 A large railway network suffers points failures at an average rate of 1 every 3 days. Assume that the number of points failures can be modelled by a Poisson distribution. The network employs a new firm of engineers. After the new engineers have become established, it is found that in a randomly chosen period of 15 days there are 2 instances of points failures.

1. Test, at the \(5 \%\) significance level, whether there is evidence that the mean number of points failures has been reduced.
2. A new test is carried out over a period of 150 days. Use a suitable approximation to find the greatest number of points failures there could be in 150 days that would lead to a \(5 \%\) significance test concluding that the average number of points failures had been reduced.