Changes in airport procedures require considerable planning. Arrival rates of aircraft are important factors that must be taken into account. Suppose small aircraft arrive at a certain airport, according to a Poisson process, at the rate of 6 per hour. Thus, the Poisson parameter for arrivals over a period of hours is μ = 6t.
If we define a working day as 12 hours, what is the probability that at least 75 small aircraft arrive during a working day?
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Is there a faster way of solving the problem?