If an average of 12 12 customers are served per hour,what is the probability that the next customer will arrive in 6 minutes or less?
A)0.61
B)0.30
C)0.70
D)0.39

Question

Quizplus · Accepted Answer

First, we need to convert the given average of 12 customers per hour to the average number of customers per minute. 
12 customers/hour = 12/60 customers/minute = 0.2 customers/minute.

Now, we can use the Poisson distribution formula to calculate the probability of the next customer arriving in 6 minutes or less:

P(X ≤ 1) = e-λ(λ^0/0!) + e-λ(λ^1/1!) 
where 
X = number of customers arriving in 6 minutes 
λ = average number of customers per minute = 0.2

P(X ≤ 1) = e^-0.2(0.2^0/0!) + e^-0.2(0.2^1/1!) 
= 0.6703

Therefore, the probability of the next customer arriving in 6 minutes or less is 0.6703 or approximately 0.70. 
Hence, the best answer choice is C.

If an Average of 12 12 Customers Are Served Per