Arrivals to a bank automated teller machine (ATM) are distributed according to a Poisson distribution with a mean equal to three per 15 minutes. What is the probability that fewer than four customers will arrive in a 30-minute segment?
A) 0.1512
B) 0.1889
C) 0.2515
D) 0.2576

Question

Quizplus · Accepted Answer

The probability of fewer than four customers arriving in a 30-minute segment is the same as the probability of three or fewer customers arriving in a 30-minute segment. The mean number of arrivals in a 30-minute segment is 3 * 2 = 6. The probability of three or fewer customers arriving in a 30-minute segment is given by the Poisson distribution with mean 6:P(X <= 3) = 0.1512Therefore, the correct answer is A.

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