The number of homeruns hit during a major league baseball game follows a Poisson distribution with a mean of 3.2. Find the probability that a randomly selected game would have exactly 5
Homeruns hit.
A)0.895
B)0.219
C)0.114
D)0.105

Question

Quizplus · Accepted Answer

The probability of observing exactly $k$ events (in this case, 5 homeruns) in a Poisson distribution is given by the formula $P(X=k) = \frac{e^{-\lambda} \lambda^k}{k!}$, where $\lambda$ is the mean number of events (3.2 for this problem), and $k$ is the number of events of interest (5 homeruns). Plugging in the values, we get $P(X=5) = \frac{e^{-3.2} * 3.2^5}{5!}$, which calculates to approximately 0.114.

The Number of Homeruns Hit During a Major League Baseball