Customers are serviced at a rate of five customers per hour according to an exponential distribution. What is the probability that customer service will require fewer than 20 minutes?
A) less than or equal to 0.75
B) greater than 0.75 but less than or equal to 0.80
C) greater than 0.80 but less than or equal to 0.85
D) greater than 0.85

Question

Quizplus · Accepted Answer

The rate is 5 customers per hour, so the mean service time is 1/5 hours (12 minutes). The probability that service time is less than 20 minutes (1/3 hour) is 1 - e^(-5*(1/3)) = 1 - e^(-5/3) ≈ 0.81, which falls in the range greater than 0.80 but less than or equal to 0.85.

Customers Are Serviced at a Rate of Five Customers Per