The number of road construction projects that take place at any one time in a certain city follows a Poisson distribution with a mean of 6. Find the probability that exactly three road construction projects are currently taking place in this city.
A) 0.050409
B) 0.014936
C) 0.089235
D) 0.301168

Question

Quizplus · Accepted Answer

The probability of observing exactly k events in a Poisson distribution is given by the formula P(X=k) = (λ^k * e^(-λ)) / k!, where λ is the average rate (mean) and k is the number of events. Here, λ = 6 and k = 3. Calculating this gives P(X=3) = (6^3 * e^(-6)) / 3! = 0.089235.

The Number of Road Construction Projects That Take Place at Any