Use the Poisson Distribution to find the indicated probability. Round to three decimal places when necessary.
-$\lambda = 4.5 ; \mathrm { P } ( \mathrm { X }

Question

Use the Poisson Distribution to find the indicated probability. Round to three decimal places when necessary.
-$\lambda = 4.5 ; \mathrm { P } ( \mathrm { X } < 3 )$  
A)$0.174$
B) $0.162$
C) $0.504$
D) $0.169$

Quizplus · Accepted Answer

The Poisson distribution formula for finding the probability of observing $x$ events in a fixed interval of time or space is given by $P(X = x) = \frac{e^{-\lambda} \lambda^x}{x!}$, where $\lambda$ is the average number of events in the given interval, and $x$ is the number of occurrences. To find $P(X < 3)$, we need to calculate $P(X = 0) + P(X = 1) + P(X = 2)$ with $\lambda = 4.5$. Calculating each and summing them gives a result close to $0.174$.

Use the Poisson Distribution to Find the Indicated Probability λ=4.5;P(X<3)\lambda = 4.5 ; \mathrm { P } ( \mathrm { X } < 3 )λ=4.5;P(X<3)

Use the Poisson Distribution to Find the Indicated Probability $\lambda = 4.5 ; \mathrm { P } ( \mathrm { X } < 3 )$