Exhibit 5-15.A bank manager estimates that an average of two customers enter the tellers' queue every five minutes.Assume that the number of customers that enter the tellers' queue is Poisson-distributed. Refer to Exhibit 5-15.What is the probability that at least two customers enter the queue in a randomly selected five-minute period?
A)0.1353
B)0.2707
C)0.4060
D)0.5940

Question

Quizplus · Accepted Answer

The Poisson distribution formula is P(X=x) = (e^(-λ) * λ^x) / x!
Where λ is the mean number of occurrences per time interval, and x is the number of occurrences we're interested in.
In this case, λ = 2, x ≥ 2 because we want to find the probability of at least two customers entering the queue, we can use the formula to calculate the probability as follows:
P(X ≥ 2) = 1 - P(X = 0) - P(X = 1)
= 1 - (e^(-2) * 2^0) / 0! - (e^(-2) * 2^1) / 1!
= 1 - (e^(-2) + 2e^(-2))
= 1 - 0.4060
= 0.5940
Therefore, the best choice is D, with the probability of 0.5940.