If an average of 12 customers is 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

To solve this problem, we need to first find the average time between customers.

Average time between customers (in minutes) = 60 minutes/hour ÷ 12 customers/hour = 5 minutes/customer

Next, we need to find the probability that the next customer will arrive in 3 minutes or less.

To do this, we will use the exponential distribution with a rate parameter of 1/5 (since the average time between customers is 5 minutes):

P(X ≤ 3) = 1 - e^(-1/5 * 3) = 0.4493

Therefore, the probability that the next customer will arrive in 3 minutes or less is approximately 0.45.

The best choice is C.

If an Average of 12 Customers Is Served Per Hour