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 3. Find the probability that more than four road construction
Projects are currently taking place in the city.
A)0.815263
B)0.184737
C)0.352768
D)0.647232

Question

Quizplus · Accepted Answer

The probability of more than four road construction projects occurring is found by subtracting the probability of four or fewer projects from 1. The Poisson distribution formula for the probability of exactly k events is (λ^k * e^(-λ))/k!, where λ is the mean number of events (3 in this case), e is the base of the natural logarithm, and k! is the factorial of k. To find the probability of more than four projects, calculate the cumulative probability for 0 to 4 projects and subtract from 1. The correct answer, after performing these calculations, is approximately 0.184737, indicating a relatively low probability of having more than four road construction projects simultaneously.

The Number of Road Construction Projects That Take Place at Any