Question

Doctors at a particular clinic never see a patient on time. The amount of time (in minutes)

past the appointment time that a patient must wait to see a doctor has an exponential distribution with λ = .027.

a) What is the variance of the amount of time the patient will have to wait beyond the appointment time?

b) Compute the probability that the doctor will see the patient less than 40 minutes after the appointment time?

Answer 1

Let X denote the amount of time, in minutes, past the appointment time that a patient must wait to see a doctor at the clinic.

Now, we are given that X has an exponential distribution with λ = 0.027, thus we get:

X ~ Exponential(λ = 0.027) and the cumulative distribution function of X is given by:

a)

The variance of the amount of time the patient will have to wait beyond the appointment time is given by:

b)

The probability that the doctor will see the patient less than 40 minutes after the appointment time is given by:

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