The number of lightning strikes in a year at the top of a particular mountain has a Poisson distribution with a mean of 3.9. Find the probability that in a randomly selected year, the number of lightning strikes is 2.
A)0.2617
B)0.1539
C)0.0128
D)0.2001

Question

Quizplus · Accepted Answer

The probability of observing exactly $k$ events in a Poisson distribution is given by $P(X=k) = \frac{e^{-\lambda} \lambda^k}{k!}$, where $\lambda$ is the mean number of events. Here, $\lambda = 3.9$ and $k = 2$. Plugging these values into the formula gives $P(X=2) = \frac{e^{-3.9} \cdot 3.9^2}{2!} = 0.1539$.

The Number of Lightning Strikes in a Year at the Top