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  3. a doctor has scheduled two appointments, one at 1p

A doctor has scheduled two appointments, one at 1pm and the other at 1:30pm. The amount...

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Basic Math

A doctor has scheduled two appointments, one at 1pm and theother at 1:30pm. The amount of time the doctor spends with thepatient is a constant 20 minutes plus a random amount of time whichis distributed as exponential with mean 8 minutes. Assume that bothpatients will be on time for their appointments.

  1. What is the chance the doctor will be late for her 1:30appointment because she spends more than 30 minutes with her 1pmappointment?
  2. On average, how long will the 1:30 appointment be at thedoctor’s office?

The time the 1:30 appointment spendsin the office is the sum of 3 parts: the random waiting time W, theconstant 20 minutes of examination time and the additional randomexamination time T.

We seek E[W + 20 + T] = E[W] + 20 +E[T]

To determine the E[W], condition onwhether or not the 1:00pm appointment is still going on at1:30pm.

Explanations with answers please

Answer & Explanation Solved by verified expert
4.4 Ratings (920 Votes)
aLet T1 be therandom amount of time taken by patientappointed at 1 pm Then T1 Exp 18The doctor spends more than 30 minutes with her    See Answer
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