The number of road construction projects that take place at any one time in a certain city follows a Poissondistribution with a mean of 5. Find the probability that exactly six road construction projects are currentlytaking place in this city.
A) 0.146223
B) 0.322754
C) 0.072770
D) 0.160623

Question

Quizplus · Accepted Answer

The probability of exactly k events in a Poisson distribution is given by $P(k) = \frac{\lambda^k e^{-\lambda}}{k!}$, where $\lambda$ is the mean number of events. Here, $\lambda = 5$ and $k = 6$, so $P(6) = \frac{5^6 e^{-5}}{6!} \approx 0.146223$.

The Number of Road Construction Projects That Take Place at Any