6 The number of sports injuries per month at a certain college has a Poisson distribution. In the past the mean has been 1.1 injuries per month. The principal recently introduced new safety guidelines and she decides to test, at the \(2 \%\) significance level, whether the mean number of sports injuries has been reduced. She notes the number of sports injuries during a 6-month period.

1. Find the critical region for the test and state the probability of a Type I error.
2. State what is meant by a Type I error in this context.
3. During the 6 -month period there are a total of 2 sports injuries. Carry out the test.
4. Assuming that the mean remains 1.1 , calculate the probability that there will be fewer than 30 sports injuries during a 36-month period.