Literature shows that the incidence of breast cancer is 150 cases per 100,000 women aged 45-49 years old annually. The researchers want to test whether regular intake of vitamin D would reduce 20% of the risk of the occurence of breast cancer. They plan to recruit women aged 45-49 years who are free of breast cancer at the beginning and randomly assign them into two groups, i.e., group one: women in this group will receive vitamin D treatment, and group two: women in this group will receive placebo.

a) if the ratio is 1:1, the significant level is set at 0.05 with 85% of power, how many women aged 45-49 years are needed for this study?