Suppose that the arrival time of a patient to a doctor’s appointment—relative to

Question

Suppose that the arrival time of a patient to a doctor’s appointment—relative to the original appointment time—is normally distributed with a mean of -5 minutes and a standard deviation of 5 minutes, for which positive values indicate the patient is late for their appointment.

a. What is the probability that a randomly selected patient is late to his or her originally scheduled appointment? Report any equations or Excel functions that you use to answer this question.

b. Assume that there are 40 patients scheduled for each day of the week. Let X represent the number of patients in this sample who are late for their appointment. What is the expected value of X, and what is the probability that X is at least five (i.e., at least five patients on a given day are late for their appointments)? Again, report any equations or Excel functions that you use to answer this question.

Explanation / Answer

a.) X : the arrival time of a patient to a doctor’s appointment—relative to the original appointment time

X ~ N( -5 , 5^2)

a.) P( selected patient is late)

= P( X > 0)

= P( Z > ( 0 + 5)/5))

= P(Z > 1)

= 0.1587

b.) X :number of patients in this sample who are late for their appointment

E( X) = 40 × P( the patient is late) = 40 × 0.1587 = 6.348

P( X >= 5)

= P( Z >= (5 - 6.348)/(40 × 0.1587 × 0.8413))

= P( Z >= -0.5833)

= 0.7202

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