1 A low-cost airline charges for breakfasts on its early morning flights. On average, \(10 \%\) of passengers order breakfast.
- Find the probability that, out of 8 randomly selected passengers, exactly 1 orders breakfast.
- Use a suitable Poisson approximating distribution to find the probability that the number of breakfasts ordered by 30 randomly selected passengers is
(A) exactly 6,
(B) at least 8 . - State the conditions under which the use of a Poisson distribution is appropriate as an approximation to a binomial distribution.
- The aircraft carries 120 passengers and the flight is always full. Find the mean \(\mu\) and variance \(\sigma ^ { 2 }\) of a Normal approximating distribution suitable for modelling the total number of passengers on the flight who order breakfast.
- Use your Normal approximating distribution to calculate the probability that more than 15 breakfasts are ordered on a particular flight.
- The airline wishes to be at least \(99 \%\) certain that the plane will have sufficient breakfasts for all passengers who order them. Find the minimum number of breakfasts which should be carried on each flight.