Breakdowns occur on a particular machine at random at a mean rate of 1.25 per week.
Find the probability that fewer than 3 breakdowns occurred in a randomly chosen week.
Over a 4 week period the machine was monitored. During this time there were 11 breakdowns.
Test, at the \(5 \%\) level of significance, whether or not there is evidence that the rate of breakdowns has changed over this period. State your hypotheses clearly.