Final answer:
The requested percentage of U.S. local health departments with a local board of health from the 2016 profile is not provided in the reference material, and therefore cannot be accurately answered.
Step-by-step explanation:
The percentage of U.S. local health departments that reported the presence of a local board of health in the 2016 profile conducted by the National Association of County and City Health Officials is not explicitly provided in the given reference material. To find the correct percentage, one would need to access the specific report or dataset from that year, which is not included in the provided excerpts. Without the exact figure from the 2016 profile, it is inappropriate to guess among the percentages listed in the question (75%, 95%, 55%, 35%). Professionalism requires providing information based on evidence and factual data, thus in this instance, it is not possible to provide a substantiated answer.