With the development of COVID19 vaccines, the authority is planning to have a viable vaccination programme for the mass. However, they need to perform a simulation prior to scheduling the residents on their vaccination appointments. Generally, the process to get one's vaccination at the designated clinic involves going through three (3) stations: Registration, Health Check and Vaccine Injection.

Table 4-1, 4-2 and 4-3 show the probability distribution for the processing time at the Registration, Health Check and Vaccine Injection stations, respectively.

(a) Identify the corresponding interval of random numbers (in decimals) for the processing time at the Registration, Health Check and Vaccine Injection stations using the probability information in Table 4-1, 4-2 and 4-3. Present your answer in three (3) separate tables.

(b) Using the interval in Question 4(a), state the average total processing time based on the following five (5) vaccine recipients by simulating their processing time at the Registration, Health Check and Vaccine Injection stations, respectively represented by a set of 3 random number:

i.Recipient 1 - 0.23, 0.43, 0.86

ii.Recipient 2 - 0.18, 0.28, 0.68

iii.Recipient 3 - 0.52, 0.13, 0.26

iv.Recipient 4 - 0.61, 0.76, 0.16

v.Recipient 5 - 0.91, 0.32, 0.39

(c) Identify and explain any two (2) additional information needed if the authority is interested to know the recipient's time spent waiting for their turn at each station.

Table 4-1 Processing time at Registration Station Probability in minutes 0.30 0.20 0.25 0.15 0.10 Processing time at Health Check Station Probability in minutes Table 4-3 Processing time at Vaccine Injection Probability Station in minutes -