Please do it and be as specific as possible on processes.

2. Suppose a medical doctor suspects that 98% cases of COVID-19 would show fever symptoms. In order to study whether fever is one of the most common characteristics of COVID-19, this doctor randomly collected data on 1,099 patients with laboratory-confirmed COVID-19 and the result showed that 966 patients have experienced the fever. (a) Use the doctors data to construct a 99% confidence interval for the true proportion of confirmed COVID-19 patients who had fever. [3 marks] (b) Write out the assumptions and conditions necessary for the interval you constructed in part 2a in the context of the question. [3 marks] (c) If we say "we are 99% confident the true proportion of confirmed COVID-19 patients who had fever is between the range of the interval you calculated in part (2a)". Provide an interpretation of that sentence in the context of the question. [2 marks] (d) When planning to estimate a population proportion, the doctor needs to determine the appropriate sample size. Suppose the doctor doesn't have any prior information about the proportion and desires the estimate to be correct to within 0.05 with 99% confidence, how large a sample size is needed? [3 marks]