Patients scheduled to see their primary care physician at a particular hospital wait, on average, an additional eight minutes after their appointment is scheduled to start. Assume the time that patients wait is exponentially distributed. What is the probability a randomly selected patient will see the doctor within five minutes of the scheduled time?
A) 0.2019
B) 0.4647
C) 0.5353
D) 0.7981

Question

Quizplus · Accepted Answer

Let X be the time (in minutes) a patient waits after their appointment is scheduled to start. 
We know that the average waiting time is 8 minutes, therefore lambda = 1/8. 
We are looking for P(X ≤ 5), which can be calculated using the exponential CDF with lambda = 1/8: 
P(X ≤ 5) = 1 - e^(-5/8) ≈ 0.4647. 
Therefore, the answer is B.

Patients Scheduled to See Their Primary Care Physician at a Particular