Poisson distribution problem?

Question

with Lambda = 4, wich is the probability of more than 5?

I stated it as: 1 - P (x <= 5) but apparently it was wrong...

Answer 1

Find the probability of more than 5 occurrences given the mean λ = 4.

For the Poisson distribution the probability of k occurrences given mean λ is:

P(k | λ) = [e^(-λ)](λ^k) / k!
___________

P(k > 5) = 1 - P(k ≤ 5)

P(k > 5) = 1 - 0.785130387 = 0.214869613

Answer 2

P(x > 5) = 1 - P(x<=5)

P(x <= 5) = P(x=0) + P(x=1) + P(x=2) + P(x=3) + P(x=4) + P(x=5)

You might find this sum in math tables somewhere (sometimes they have cumulative sums of the Poisson distribution), but if not,

P(x<=5) = 0.018 + 0.073 + 0.146 + 0.195 + 0.195 + 0.156 = 0.785

So P(x > 5) = 1 - 0.785 = 0.215