Use the Poisson Distribution to find the indicated probability. Round to three decimal places when necessary.
-$$\lambda = 0.466 ; \mathrm { P } ( \mathrm { X } = 2 )$$
A)$0.006$
B) $0.085$
C) $0.068$
D) $0.173$

Question

Use the Poisson Distribution to find the indicated probability. Round to three decimal places when necessary.
-$$\lambda = 0.466 ; \mathrm { P } ( \mathrm { X } = 2 )$$  
A)$0.006$
B) $0.085$
C) $0.068$
D) $0.173$

Quizplus · Accepted Answer

The Poisson probability of exactly $k$ events in an interval is given by $P(X=k) = \frac{e^{-\lambda} \lambda^k}{k!}$. For $\lambda = 0.466$ and $k = 2$, $P(X=2) = \frac{e^{-0.466} \cdot 0.466^2}{2!} \approx 0.068$.

Use the Poisson Distribution to Find the Indicated Probability λ=0.466;P(X=2)\lambda = 0.466 ; \mathrm { P } ( \mathrm { X } = 2 )λ=0.466;P(X=2)

Use the Poisson Distribution to Find the Indicated Probability $\lambda = 0.466 ; \mathrm { P } ( \mathrm { X } = 2 )$