The number of goals scored at each game by a certain hockey team follows a Poisson distribution with a mean of 6 goals per game. Find the probability that the team will score more than three
Goals during a game.
A)0.848796
B)0.151204
C)0.061969
D)0.938031

Question

Quizplus · Accepted Answer

The probability of scoring more than three goals in a game is found by subtracting the probability of scoring three or fewer goals from 1. The Poisson distribution formula for the probability of observing k events (goals in this case) is P(k; λ) = (e^(-λ) * λ^k) / k!, where λ is the average number of events (6 goals per game in this case), and k is the number of events of interest. To find the probability of scoring more than three goals, calculate the cumulative probability for 0, 1, 2, and 3 goals and subtract from 1. The correct answer is obtained by using the Poisson cumulative distribution function or calculating each probability individually and summing them up. The result is approximately 0.848796, indicating a high likelihood of scoring more than three goals in a game.

The Number of Goals Scored at Each Game by a Certain