The number of goals scored at each game by a certain hockey team follows a Poisson distribution with a mean of 5 goals per game. Find the probability that the team scored exactly three goals in each of four randomly selected games.
A) 0.00038828
B) 0.56149561
C) 0.00540243
D) 0.43850439

Question

Quizplus · Accepted Answer

The probability of scoring exactly three goals in a game is given by the Poisson distribution:P(X = k) = (e^-λ * λ^k) / k!where λ is the mean number of goals per game.In this case, λ = 5, so the probability of scoring exactly three goals in a game is:P(X = 3) = (e^-5 * 5^3) / 3! = 0.14038The probability of scoring exactly three goals in each of four randomly selected games is:P(X = 3)^4 = 0.00038828Therefore, the correct answer is A.

The Number of Goals Scored at Each Game by a Certain