4 The number of accidents per month at a certain road junction has a Poisson distribution with mean 4.8. A new road sign is introduced warning drivers of the danger ahead, and in a subsequent month 2 accidents occurred.

1. A hypothesis test at the \(10 \%\) level is used to determine whether there were fewer accidents after the new road sign was introduced. Find the critical region for this test and carry out the test.
2. Find the probability of a Type I error.
   \(5 X\) and \(Y\) are independent random variables each having a Poisson distribution. \(X\) has mean 2.5 and \(Y\) has mean 3.1.
3. Find \(\mathrm { P } ( X + Y > 3 )\).
4. A random sample of 80 values of \(X\) is taken. Find the probability that the sample mean is less than 2.4.