The number of traffic accidents that occur on a particular stretch of road during a month follows a Poisson distribution with a mean of 7.2. Find the probability that exactly five accidents will occur on this stretch of road each of the next two months.
A) 0.014492
B) 0.120382
C) 0.240764
D) 0.002876

Question

Quizplus · Accepted Answer

The probability of exactly k events in a Poisson distribution is given by $ P(X = k) = \frac{e^{-\lambda} \lambda^k}{k!} $. For one month, $ \lambda = 7.2 $ and $ k = 5 $. Calculate this probability and then square it for two months: $ \left(\frac{e^{-7.2} \cdot 7.2^5}{5!}\right)^2 \approx 0.014492 $.

The Number of Traffic Accidents That Occur on a Particular