The number of lightning strikes in a year at the top of a particular mountain has a Poisson distribution with a mean of 2.8.Find the probability that in a randomly selected year,the number of lightning strikes is 2.
A)0.3099
B)0.7616
C)0.2384
D)0.0199
E)0.4052

Question

Quizplus · Accepted Answer

The Poisson distribution is given by $P(X=k)=\frac{\lambda^k e^{-\lambda}}{k!}$, where $X$ is the random variable denoting the number of lightning strikes, $\lambda$ is the mean of the distribution. Here, we have $\lambda=2.8$, and we need to find $P(X=2)$.
$P(X=2)=\frac{2.8^2 e^{-2.8}}{2!} \approx \boxed{0.2384}$

The Number of Lightning Strikes in a Year at the Top