The way you answered it is by finding P(x = 2). The question asks for the ulative number up to 2. The only way that you can do it by hand is to use calculus, or alternatively you could use a calculator (probably a graphing calc) to find the ulative probablity, that is, the probability of x being less than or equal to two. To do that, most calculators that have poisson would be to use the poissoncdf
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