Final answer:
a) Elevated serum creatine kinase levels
In a patient with symmetrical, proximal muscle weakness and biopsy showing muscle fiber necrosis, the most likely additional finding would be elevated serum creatine kinase levels, indicating muscle damage.
Step-by-step explanation:
A 50-year-old woman with symmetrical, proximal muscle weakness and a deltoid biopsy showing lymphocytic infiltrate with focal necrosis likely has an inflammatory myopathy.
With her antinuclear antibody (ANA) test being negative, a common additional finding would be elevated serum creatine kinase levels, which is a diagnostic indicator of muscle damage and is typically elevated in conditions like polymyositis and dermatomyositis.
Autoantibodies such as anti-Jo-1 are also associated with these conditions, especially in the presence of interstitial lung disease. However, since only one choice is appropriate and considering the provided options, elevated serum creatine kinase levels would be the most likely additional finding in this patient.