1. 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 34 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 0.05. How large a sample should she take to achieve this? Please carry answers to at least six decimal places in intermediate steps.

Sample size =___________