Dwight Howard plays center in the National Basketball Association and averaged 1.8 blocked shots per game during a recent season. Assume that the number of blocked shots per game follows the Poisson distribution. What is the probability that Dwight Howard will block exactly two shots during the first half of the next game?

Question

Quizplus · Accepted Answer

The Poisson distribution formula for the probability of observing exactly $k$ events (in this case, blocked shots) is given by $P(k) = \frac{\lambda^k e^{-\lambda}}{k!}$, where $\lambda$ is the average rate of occurrence over the interval of interest. Since Howard averages 1.8 blocked shots per game, for half a game, $\lambda = 1.8 / 2 = 0.9$. Plugging in the values for exactly 2 blocked shots ($k = 2$) gives $P(2) = \frac{0.9^2 e^{-0.9}}{2!} = 0.1647$.

Dwight Howard Plays Center in the National Basketball Association and Averaged