Final answer:
The task that can be delegated to an assistive personnel is weighing a newly admitted client who has anorexia nervosa, as it does not require clinical judgment or intervention.
Step-by-step explanation:
The nurse in an inpatient mental health facility can delegate tasks that do not require nursing judgment or intervention to assistive personnel (AP). The appropriate task from the options provided to delegate to an AP is weighing a newly admitted client who has anorexia nervosa.
This is a straightforward task that can be safely performed by the AP under the nurse's supervision. However, updating the plan of care for a client, leading a medication education group, and conducting a mental status exam are all tasks that require specific clinical training and judgment, which are responsibilities of the registered nurse or licensed practical nurse and cannot be delegated to an AP.