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 will score more than three goals during a game.
A) 0.124652
B) 0.734974
C) 0.265026
D) 0.875348

Question

Quizplus · Accepted Answer

The probability of scoring more than three goals is the complement of the probability of scoring three goals or less. The probability of scoring three goals or less is the sum of the probabilities of scoring 0, 1, 2, or 3 goals. Using the Poisson distribution, we can calculate these probabilities as follows:P(X = 0) = e^-5 * 5^0 / 0! = 0.006738P(X = 1) = e^-5 * 5^1 / 1! = 0.03369P(X = 2) = e^-5 * 5^2 / 2! = 0.08423P(X = 3) = e^-5 * 5^3 / 3! = 0.13372Therefore, the probability of scoring three goals or less is:P(X <= 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.006738 + 0.03369 + 0.08423 + 0.13372 = 0.265026And the probability of scoring more than three goals is:P(X > 3) = 1 - P(X <= 3) = 1 - 0.265026 = 0.734974

The Number of Goals Scored at Each Game by a Certain