A statistics 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 two students will arrive.
A)0.2241
B)0.6091
C)0.1992
D)0.5415

Question

Quizplus · Accepted Answer

The probability of exactly k events in a Poisson distribution is given by $P(k; \lambda) = \frac{e^{-\lambda} \lambda^k}{k!}$, where $\lambda$ is the average rate (3 students in this case) and $k$ is the number of events (2 students). Plugging in the values: $P(2; 3) = \frac{e^{-3} 3^2}{2!} = 0.2241$.

A Statistics Professor Finds That When He Schedules an Office