If an average of 12 customers are served per hour,what is the probability that the next customer will arrive in 3 minutes or less?
A)0.55
B)0.30
C)0.45
D)0.39

Question

Quizplus · Accepted Answer

First, we need to convert the given average into a rate of arrival per minute.

Rate of arrival per minute = 12 customers per hour / 60 minutes per hour = 0.2 customers per minute

Now we can use the Poisson distribution formula to calculate the probability of the next customer arriving in 3 minutes or less:

P(x ≤ 1) = e^(-λ) * λ^(x=0 or 1) / x!

P(x ≤ 1) = e^(-0.6) * 0.6^0/0! + e^(-0.6) * 0.6^1/1!

P(x ≤ 1) = 0.5488 ≈ 0.55

Therefore, the probability that the next customer will arrive in 3 minutes or less is approximately 0.55 or 55%, which corresponds to choice C.

If an Average of 12 Customers Are Served Per Hour,what