Customers are serviced at a rate of three customers per hour according to an exponential distribution.What is the probability that customer service will require fewer than 10 minutes?
A) Less than or equal to 0.40
B) Greater than 0.40 but less than or equal to 0.45
C) Greater than 0.45 but less than or equal to 0.50
D) Greater than 0.50

Question

Quizplus · Accepted Answer

Since the customers are serviced at a rate of 3 per hour, this is equivalent to a service time of 20 minutes per customer (60 minutes divided by 3 customers). Thus, the service time follows an exponential distribution with a mean of 20 minutes. We want to find the probability that the service time is less than 10 minutes. 
Using the exponential distribution formula, we get: 
P(X < 10) = 1 - e^(-10/20) = 1 - e^(-0.5) ≈ 0.393 
Therefore, the probability that customer service will require fewer than 10 minutes is less than or equal to 0.40, which is choice A.

Customers Are Serviced at a Rate of Three Customers Per