Use the Poisson probability function to find P(3

Question

Use the Poisson probability function to find P(3 < x < 5), where λ = 2.
A).2497
B).3067
C).1961
D).1789
E).4282

Quizplus · Accepted Answer

The Poisson probability function for a given number of occurrences $k$ is $P(k) = \frac{e^{-\lambda} \lambda^k}{k!}$, where $\lambda$ is the average number of occurrences. To find $P(3 < x < 5)$, we calculate $P(x=4)$ because $P(3 < x < 5)$ means $x$ can only be 4 in this discrete distribution. Using $\lambda = 2$, $P(4) = \frac{e^{-2} 2^4}{4!} = \frac{e^{-2} 16}{24} = \frac{2^4}{e^2 4!}$. Calculating this gives approximately 0.0902 or 9.02%, which is not directly listed. However, the correct approach involves summing probabilities for the exact value, which seems to have been misunderstood in the options provided. The correct calculation for a range would involve summing over the range, but for $3 < x < 5$, it's directly $P(x=4)$. Given the options, none directly match the correct calculation for $P(3 < x < 5)$ based on the Poisson distribution formula, suggesting a possible misunderstanding in the question's setup or in interpreting the options provided.

Use the Poisson Probability Function to Find P(3 < X