(Solved): Refer to the following scenario. An epidemiologist is worried about the prevalence of the flu in Ea ...

Refer to the following scenario. An epidemiologist is worried about the prevalence of the flu in East Vancouver and the potential shortage of vaccines for the area. She will need to provide a recommendation for how to allocate the vaccines appropriately across the city. She takes a simple random sample of 338 people living in East Vancouver and finds that 32 have recently had the flu. Suppose that the epidemiologist wants to re-estimate the population proportion and wishes for her $95\%$ confidence interval to have a margin of error no larger than 0.04. How large a sample should she take to achieve this? Please carry answers to at least six decimal places in intermediate steps. Sample size $=$