A statistics professor finds that when he schedules an office hour at the 10:30 a.m. time slot, an average of three students arrives. Use the Poisson distribution to find the probability that in a randomly selected office hour no
Students will arrive.
A)0.0498
B)0.1225
C)0.1108
D)0.0743

Question

Quizplus · Accepted Answer

The probability that no students will arrive during a randomly selected office hour, given an average arrival rate ($\lambda$) of 3 students, can be calculated using the Poisson distribution formula for $k = 0$ events: $P(X=k) = \frac{e^{-\lambda} \lambda^k}{k!}$. Substituting $\lambda = 3$ and $k = 0$, we get $P(X=0) = \frac{e^{-3} 3^0}{0!} = e^{-3} \approx 0.0498$.

A Statistics Professor Finds That When He Schedules an Office