Final answer:
The needed hours of nursing care for the 3 to 11 PM shift is 61 hours.
Step-by-step explanation:
The needed hours of nursing care can be calculated by multiplying the number of clients in each category by the allotted hours for that category and summing them up. Category I has 4 clients at 2.0 hours each, which totals to 8.0 hours. Category II has 2 clients at 2.3 hours each, which totals to 4.6 hours. Category III has 10 clients at 2.8 hours each, which totals to 28.0 hours. Category IV has 6 clients at 3.4 hours each, which totals to 20.4 hours. Adding all these hours together, the needed hours of nursing care is 61 hours. Therefore, the correct answer is option 3) 61 hours.