The number of traffic accidents per day on a certain section of highway is thought to be Poisson distributed with a mean equal 2.19. Then the probability of no accidents on this section of highway during one day period is approximately:
A) 0.457
B) 0.112
C) 0.318
D) 0.296
E) 0.211

Question

Quizplus · Accepted Answer

The Poisson distribution with mean $\lambda$ is given by:

$$P(X=k)=\frac{e^{-\lambda}\lambda^k}{k!}$$

In this case, we have $\lambda=2.19$ and we want to find $P(X=0)$:

$$P(X=0)=\frac{e^{-2.19}(2.19)^0}{0!}\approx 0.112$$

Therefore, the best choice is (B) with probability approximately 0.112.

The Number of Traffic Accidents Per Day on a Certain