Compute Probabilities of a Poisson Random Variable
-The number of goals scored at State College hockey games follows a Poisson distribution with a mean of 7 goals per game. Find the probability that a randomly selected State College hockey game would have more than three goals scored.
A) 0.918235
B) 0.081765
C) 0.970364
D) 0.029636

Question

Quizplus · Accepted Answer

The probability of more than three goals means we need to find 1 minus the probability of 3 or fewer goals. The Poisson probability formula is P(X=k) = (λ^k * e^(-λ)) / k!, where λ is the mean number of successes (7 in this case), k is the number of successes, and e is the base of the natural logarithm. To find the probability of 3 or fewer goals, we calculate P(X=0), P(X=1), P(X=2), and P(X=3), and sum these probabilities. Then, we subtract this sum from 1 to find the probability of more than three goals. Calculating this directly or using a Poisson distribution table/calculator will give us the probability of more than three goals as approximately 0.918235.