7 All the seats on a certain daily flight are always sold. The number of passengers who have bought seats but fail to arrive for this flight on a particular day is modelled by the distribution \(\mathbf { B } ( 320,0.005 )\).
- Explain what the number 320 represents in this context.
- The total number of passengers who have bought seats but fail to arrive for this flight on 2 randomly chosen days is denoted by \(X\). Use a suitable approximating distribution to find \(\mathrm { P } ( 2 < X < 6 )\).
- Justify the use of your approximating distribution.
After some changes, the airline wishes to test whether the mean number of passengers per day who fail to arrive for this flight has decreased. - During 5 randomly chosen days, a total of 2 passengers failed to arrive. Carry out the test at the 2.5\% significance level.
If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.