7 The number of planes arriving at an airport every hour during daytime is modelled by the random variable \(X\) with distribution \(\operatorname { Po } ( 5.2 )\).
- State two assumptions required for the Poisson model to be valid in this context.
- (a) Find the probability that the number of planes arriving in a 15 -minute period is greater than 1 and less than 4,
(b) Find the probability that more than 3 planes will arrive in a 40-minute period. - The airport has enough staff to deal with a maximum of 60 planes landing during a 10-hour day. Use a suitable approximation to find the probability that, on a randomly chosen 10-hour day, staff will be able to deal with all the planes that land.