Per CPS, you can apply with your Norridge address.
Students do not have to live in the city of Chicago in order to apply and participate in the selection process for the Selective Enrollment schools and programs, magnet schools and programs, and open enrollment schools.
However, students DO have to live in the city of Chicago in order to enroll in and attend these schools, as well as any other Chicago public school. Proof of residency is required by July 1st of the year that the student will enroll.
There are streets in the vicinity of Norridge that are actually city of Chicago, if you look carefully how the city limits are marked, there are a couple of ‘islands’ surrounded by Chicago city.