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 have to wait more than 10 minutes?
A) 0.2865
B) 0.4493
C) 0.5507
D) 0.7135

Question

Quizplus · Accepted Answer

Since the wait time follows an exponential distribution, we can use the formula P(X > x) = e^(-λx), where λ is the rate parameter equal to 1/8 (since patients wait an average of 8 minutes longer than their scheduled appointment). Plugging in x = 10, we get P(X > 10) = e^(-10/8) = 0.2865. Therefore, the probability that a randomly selected patient will have to wait more than 10 minutes is 0.2865, or approximately 28.65%. Choice A is the correct answer.

Patients Scheduled to See Their Primary Care Physician at a Particular