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**downthesun01** *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?

Ok, the new $\displaystyle \lambda =72$

But how do I find $\displaystyle pr(X\geq 75)$?

I know that $\displaystyle pr(X\geq 75)=1-pr(X\leq 74)$

but it seems very time consuming to have to find $\displaystyle pr(X=0), pr(X=1),...,pr(X=73), pr(X=74)$

Is there a faster way of solving the problem?