Final answer:
The probability of exactly 2 accidents occurring at a busy intersection with a mean of 3.6 accidents per week, according to the Poisson distribution, is approximately 17.67%, which rounds to option D) 0.183.
Step-by-step explanation:
The probability that exactly 2 accidents will occur in a busy intersection that has accidents following a Poisson distribution with a mean (λ) of 3.6 per week can be calculated using the Poisson probability formula:
P(X=k) = (λ^k * e^-λ) / k!
Where k is the exact number of accidents we want to find the probability for, in this case, k=2.
P(X=2) = (3.6^2 * e^-3.6) / 2! = (12.96 * 0.027323) / 2 = 0.35345488 / 2 = 0.17672744.
Therefore, the probability that exactly two accidents will occur is approximately 0.1767 or 17.67%, which corresponds to the option D) 0.183 after rounding to three decimal places.