Question

Outpatient clinics are hospital clinics that have appointments for patients who visit the hospital without being admitted. At one particular clinic, it is known that the distribution of appointment times (in hours), X, is described by the cumulative distribution function

FX(x) = k − e ^{−x 2}, x ≥ 0.

(a) (Original phrasing) One particular patient must complete a 30 minute exercise program during their appointment. Show that the probability this patient’s appointment will then exceed one hour in total is e −3/4 ≈ 0.47 (show working)

(b) (Modified phrasing) You arrived early for an appointment and watched the previous patient enter for their appointment. You look at your watch and see that the previous patients’ appointment has been running for 30 minutes and has not yet finished. Show that the probability that the previous patients’ appointment will take longer than 1 hour is e −3/4 ≈ 0.47 (show working)

(d) Write down an expression for the average appointment time, E(X). Note: You do not have to evaluate the integral you write down. (show working)

Answer 1