Is it bad applying to a school while not knowing your major?
No. A lot of people are unsure of / have no clue what they want to major when they apply to colleges. And by a lot I really mean a lot. People who know their major may have a more concentrated range of activities, but an application that shows diverse interests can be equally good.
When you fill out the Common App, you generally have to fill out your top 3 majors for each school you apply. However, these are not restrictive to your future paths and usually do not have much meaning, unless you are applying to a special program / school within the university, such as engineering or Wharton, etc.