No. At 80% or at 60%, the patient is more likely sick than not, and with both mistakes equally bad, the treatment goes ahead either way: whatever the Z-ray shows, nothing changes. Baron, Beattie and Hershey gave problems like this one to 33 students in 1988, and a majority answered them correctly. The paper also reports that subjects evaluated questions as worth asking even when no answer could change the hypothesis accepted as a basis for action (Baron, Beattie & Hershey, 1988).
Baron, J., Beattie, J., & Hershey, J. C. (1988). Heuristics and biases in diagnostic reasoning: II. Congruence, information, and certainty. Organizational Behavior and Human Decision Processes, 42(1), 88-110.
Information Bias
Seeking more information even when it cannot change your decision
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