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Also, an interesting article about the top two (nurses and MDs) hints as why it's not the other way around:
Nurses are trusted more than doctors, she added, because nurses are seen as standing alongside their patients and advocating for them. “A nurse will advocate for the patient to the physician,” she said, “or help the patient talk to the physician in a certain way to address whatever the issue is.”
To some degree, that’s the inherent nature of a nurse’s role. As Feldman noted, it’s a doctor who gets blamed when things go wrong, because doctors are expected to find cures. Nurses, on the other hand, are expected to make people as comfortable as possible, to be there when needed, and to get the job done. The structure of a hospital is set up to help nurses succeed at those responsibilities, and so they are able to be reliable and trustworthy.
The breakdown by race for a lot of these professions is quite predictable: politicians (an interesting high correlation with president's party), cops, soldiers, doctors, religious leaders.