Provide a 95% CI for the true incidence rate of breast cancer over the period from age 40 to 70 in this special subgroup?

Cancer

Breast cancer is strongly influenced by a woman’s reproductive history. In particular, the longer the length of time from the age at menarche (the age when menstruation begins) to the age at first childbirth, the greater the risk is for breast cancer.

A projection was made based on a mathematical model that the 30-year risk of a woman in the general U.S. population developing breast cancer from age 40 to age 70 is 7%. Suppose a special subgroup of five hundred 40-year-old women without breast cancer was studied whose age at menarche was 17 (compared with an average age at menarche of 13 in the general population) and age at first birth was 20 (compared with an average age at first birth of 25 in the general population). These women were followed for development of breast cancer between ages 40 and 70. The study found that 18 of the women developed breast cancer between age 40 and age 70.