4 The number of cars arriving at a certain road junction on a weekday morning has a Poisson distribution with mean 4.6 per minute. Traffic lights are installed at the junction and council officer wishes to test at the \(2 \%\) significance level whether there are now fewer cars arriving. He notes the number of cars arriving during a randomly chosen 2 -minute period.

1. State suitable null and alternative hypotheses for the test.
2. Find the critical region for the test.
   The officer notes that, during a randomly chosen 2 -minute period on a weekday morning, exactly 5 cars arrive at the junction.
3. Carry out the test.
4. State, with a reason, whether it is possible that a Type I error has been made in carrying out the test in part (c).
   The number of cars arriving at another junction on a weekday morning also has a Poisson distribution with mean 4.6 per minute.
5. Use a suitable approximating distribution to find the probability that more than 300 cars will arrive at this junction in an hour.