Use the Poisson Distribution to find the indicated probability. Round to three decimal places when necessary.
-$$\lambda = 4 ; P ( X = 6 )$$
A)$0.283$
B) $0.13$
C) $0.104$
D) $0.015$

Question

Use the Poisson Distribution to find the indicated probability. Round to three decimal places when necessary.
-$$\lambda = 4 ; P ( X = 6 )$$ 
A)$0.283$
B) $0.13$
C) $0.104$
D) $0.015$

Quizplus · Accepted Answer

The Poisson probability of observing exactly $k$ events in a fixed interval of time or space is given by the formula $$P(X=k) = \frac{e^{-\lambda} \lambda^k}{k!}$$ where $\lambda$ is the average number of events (mean) and $k$ is the number of occurrences. For $\lambda = 4$ and $k = 6$, $$P(X=6) = \frac{e^{-4} 4^6}{6!} = \frac{e^{-4} 4096}{720} \approx 0.104.$$

Use the Poisson Distribution to Find the Indicated Probability λ=4;P(X=6)\lambda = 4 ; P ( X = 6 )λ=4;P(X=6)

Use the Poisson Distribution to Find the Indicated Probability $\lambda = 4 ; P ( X = 6 )$