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 more than four road construction projects are currently taking place in the city.
A) 0.714943
B) 0.848796
C) 0.151204
D) 0.285057

Question

Quizplus · Accepted Answer

The probability of more than four road construction projects taking place is given by 1 - P(0) - P(1) - P(2) - P(3) - P(4), where P(x) is the Poisson distribution with a mean of 6. Using the Poisson distribution formula, we can calculate these probabilities as follows:P(0) = e^-6 * 6^0 / 0! = 0.002479P(1) = e^-6 * 6^1 / 1! = 0.014874P(2) = e^-6 * 6^2 / 2! = 0.044622P(3) = e^-6 * 6^3 / 3! = 0.106555P(4) = e^-6 * 6^4 / 4! = 0.199640Therefore, the probability of more than four road construction projects taking place is 1 - 0.002479 - 0.014874 - 0.044622 - 0.106555 - 0.199640 = 0.714943.

The Number of Road Construction Projects That Take Place at Any