Is this a good crime story plot?

So a nurse, who uses aliases (her name isn't revealed until the end) is knowingly killing patients in a hospital. The killings escalate and detective are ordered to investigate. At the end, it is revealed that the killer nurse is actually the chief of the hospital (who is a female). It turns out she craved hands-on medical treatment as she was stuck in her office all day filling out paperwork. It ends in a hostage situation and the nurse commits suicide by drinking her own poison intended to kill a patient.