Question

There are 3.1 accidents, on average, at an intersection. Assume the variable follows a Poisson distribution. Find the probability that there will be 5 accidents at this intersection.

Answer 1

Answer:

The probability of that there will be 5 accidents at this intersection is 0.1075.

Step-by-step explanation:

The Poisson distribution is used to explain the probability distribution of the number of events in a fixed interval.

Let X = number of accidents at the intersection.

Given: X follows Poisson distribution with mean, $\lambda=3.1$

The probability distribution function of X is:

$P(X=x)=\frac{e^{-\lambda}\lambda^{x}}{x!} \\=\frac{e^{-3.1}(3.1)^{x}}{x!}$

For X = 5 the probability is:

$P(X=5)=\frac{e^{-3.1}(3.1)^{5}}{5!}\\=0.1075$

Thus, the probability of that there will be 5 accidents at this intersection is 0.1075.