Lung infections are a chronic problem for patients with cystic fibrosis (CF). Some patients with CF may have a type of bacteria called Pseudomonas aeruginosa in their lungs that can cause infections or make their symptoms worse. Tobramycin inhalation solution (TOBI) is an approved antibiotic, which is inhaled directly into the lungs, and can be used to manage these infections. Tobramycin inhalation powder (TIP) is a new, experimental powder formulation of tobramycin that is inhaled directly into the lungs using a T-326 inhaler. The purpose of this research study is to determine if TIP is safe and effective when compared to placebo (a powder with no medicine) treatment.