10 A company operates trains. The company claims that \(92 \%\) of its trains arrive on time. You should assume that in a random sample of trains, they arrive on time independently of each other.
- Assuming that \(92 \%\) of the company's trains arrive on time, find the probability that in a random sample of 30 trains operated by this company
- exactly 28 trains arrive on time,
- more than 27 trains arrive on time.
A journalist believes that the percentage of trains operated by this company which arrive on time is lower than \(92 \%\).
- To investigate the journalist's belief a hypothesis test will be carried out at the \(1 \%\) significance level. A random sample of 18 trains is selected. For this hypothesis test,
- state the hypotheses,
- find the critical region.