Compute Probabilities of a Poisson Random Variable
-A history professor finds that when he schedules an office hour at the 10:30 a.m. time slot, an average of three students arrive. Use the Poisson distribution to find the probability that in a randomly selected office hour in the 10:30 a.m. time slot exactly five students will arrive.
A) 0.1008
B) 0.0137
C) 0.0519
D) 0.0070

Question

Quizplus · Accepted Answer

The probability of exactly k arrivals in a Poisson distribution with mean λ is given by:P(X = k) = (e^-λ * λ^k) / k!In this case, λ = 3 and k = 5, so:P(X = 5) = (e^-3 * 3^5) / 5! = 0.1008