Dr Puleng is a dentist who schedules all her patients for 30 minute appointments. Some of the patients take more or less than 30 minutes depending on the type of dental work to be done. The following summary shows the various categories of work, their probabilities and the time actually needed to complete the work. Category Time Required 45 minutes Probability of Category Filling 0.40 Crown 60 minutes 0.15 Cleaning 15 minutes 0.15 Extraction 45 minutes 0.10 Check-up 15 minutes 0.20 Perform the following tasks: 3.1 Simulate what happens within the first 4 hours at the dentist's clinic 3.2 Determine average waiting time for the patients (21) (2) 3.3 Determine the idleness of the doctor. (2) Assume that all the patients show up at the clinic at exactly their scheduled arrival time starting at 8 a.m. Use the third column of random numbers from the Table of Random Numbers provided