Arrivals to a bank automated teller machine (ATM) are distributed according to a Poisson distribution with a mean equal to three per 15 minutes.Determine the probability that in a given 15- minute segment no customers will arrive at the ATM.
A) 0.0124
B) 0.0281
C) 0.0314
D) 0.0498

Question

Quizplus · Accepted Answer

The probability of no arrivals in a Poisson distribution is given by $P(X=0) = e^{-\lambda}$, where $\lambda$ is the mean number of arrivals. Here, $\lambda = 3$, so $P(X=0) = e^{-3} \approx 0.0498$.

Arrivals to a Bank Automated Teller Machine (ATM) Are Distributed