Question

1.) Calculate the probability of x = 11 successes in a Poisson experiment with a mean of μ = 14.

2.) Calculate the probability of x ≤ 6 successes in a Poisson experiment with a mean of μ = 8.

3.) Calculate the probability of x ≥ 9 successes in a Poisson experiment with a mean of μ = 7.

Answer 1

$1.~P(X=11)=\frac{e^{-14}(14)^{11}}{(11)!}=0.0844\\ 2.~P(X\leq 6)=\sum_{i=0}^6\frac{e^{-8}(8)^{i}}{i!}=0.3134 \\ 3.~P(X\geq 9)=1-\sum_{i=0}^8\frac{e^{-7}(7)^{i}}{i!}=0.2709$