THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
The number of accidents on a particular highway averages 4.4 per year.Assume that the number of accidents follows a Poisson distribution.
-What is the probability that there are exactly four accidents next year?
A)0.504
B)0.192
C)0.375
D)0.286

Question

Quizplus · Accepted Answer

We are given that accidents follow a Poisson distribution with an average of 4.4 accidents per year. 
Let λ = 4.4, then the probability of having exactly 4 accidents in a year is:

P(X=4) = (e^-λ * λ^x) / x!

P(X=4) = (e^-4.4 * 4.4^4) / 4!

P(X=4) = 0.1916

Therefore, the probability of having exactly four accidents next year is approximately 0.192, which is answer choice B.