Hi, anyone able to help me in solving these a-d? Please include working of solutions, thank you.

3. (a) A new drug treatment for migraines is manufactured at a local factory, the production line consists of two workstations and will only operate successfully if both are functioning correctly. The probability that workstation 1 functions correctly is 0.87 and the probability of whole system failure is 0.217. Using this information determine the probability that the second workstation fails. You may assume that the workstations fail independently. [4 marks] (b) Patients are recruited to take part in a trial to test the effectiveness of the migraine medication, the weight of these individuals is normally distributed with a mean of 65.8 kg and standard deviation of o = 5.4 kg. The probability that a person selected at random has a weight of between 54.4 kg and wkg (where w is a variable) is found to be 0.688, determine w. [6 marks] (c) The time between migraine attacks is recorded in days for a group of fifteen participants taking the new drug and a control group. The results are given in table 3.1. Carry out an appropriate test to determine if the medication does make an impact and there is a significant difference between the two groups at the 5% level. You may assume that the underlying populations in both instances are normally distributed. Group 1 (with medication) 12 | 20 27 32 40 14 60 61 75 100 15 68 71 77 Group 2 (without medication) 15 17 35 40 21 27 200 16 25 21 23 31 40 80 Table 3.1: Table of days between migraine attacks for those treated with the new drug and a control group.(d) The manufacturer insists that the proposed migraine medication is effective and would like to conduct another trial involving a larger sample size. They have a number of participants that have signed up for the study and will need to assign these to the treatment or control group. For the study what are the main sampling techniques that can be used for this purpose? In each case state the respective advantages of the approach. [8 marks]