3. It is suggested that a Poisson distribution with parameter \(\lambda\) can model the number of currants in a currant bun. A random bun is selected in order to test the hypotheses \(\mathrm { H } _ { 0 } : \lambda = 8\) against \(\mathrm { H } _ { 1 } : \lambda \neq 8\), using a \(10 \%\) level of significance.

1. Find the critical region for this test, such that the probability in each tail is as close as possible to \(5 \%\).
2. Given that \(\lambda = 10\), find
   1. the probability of a type II error,
   2. the power of the test.
      (4)