A04.1 Appointment durations The duration of appointments at a doctor's surgery can be assumed to be Normally distributed with expectation 10 minutes and standard deviation 3 minutes. (a) Express the probability of a randomly selected appointment taking less than 15 min- utes in terms of the standard Normal edf d. (b) Assuming independent appointment durations, derive and express in terms of & the probability that at least one of the doctor's 20 appointments will be longer than 15 minutes. (c) Are the assumptions of independence and a Normal distribution reasonable? [5]