The number of traffic accidents that occur on a particular stretch of road during a month follows a Poissondistribution with a mean of 7.5. Find the probability of observing exactly five accidents on this stretch of roadnext month.
A) 0.109375
B) 1.332455
C) 0.805166
D) 9.808925

Question

Quizplus · Accepted Answer

The probability of observing exactly $k$ accidents when the events follow a Poisson distribution with mean $\lambda$ is given by $P(X=k) = \frac{e^{-\lambda} \lambda^k}{k!}$. For $\lambda = 7.5$ and $k = 5$, the probability is $P(X=5) = \frac{e^{-7.5} * 7.5^5}{5!}$, which calculates to approximately 0.109375.

The Number of Traffic Accidents That Occur on a Particular