Dear Shiva,

he formula for a poisson is P(X = x) = e^(-lambda) lambda ^(x) / x !

lambda = mean
also with a) do mean 3 <= x <= 5,

as this is not what you wrote, assuming that what I wrote is correct then just up the values of the formula from 3 to 5, for a

P(X = 3) + P(X = 4) + P(X = 5)

i.e. e^(-4) 4 ^(3) / 3 ! + e^(-4) 4 ^(4) / 4 ! + e^(-4) 4 ^(5) / 5 !

in b, you need to obtain 1 - P (x < 3), since P(x >= 3) would require you to add up every value from 3 to infinity, which would take forever, follow the example that I provided in a) to obtain P (x < 3), remember also what the minimum possible value of X is, (i.e. 0)

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1-(3/e²)