An investigator wants to estimate the prevalence of breast cancer among women who are between 40 and 45 years of age living in Baltimore. National data suggest that 1 in 235 women are diagnosed with breast cancer by age 40. This translates to a proportion of 0.0043 (0.43%) or a prevalence of 43 per 10,000 women.

1. (15 points) Suppose the investigator wants the estimate to be within 10 per 10,000 women with 95% confidence. How many women must be involved in the study to ensure that the estimate is precise?
2. (10 points) The investigator realizes that your answer in part A is not feasible given their study budget. They decide that a sample size of 5,000 would be reasonable from a practical point of view. How precisely can we estimate the prevalence with a sample of size n=5,000?