Thank you HK for your detailed analysis of Hayashi, I learn so much from your explanations.
I never understood a point: how it can be concluded that looking at the standard deviation there must have been at least a patient with trig > 533?
Would a mathematician reach that conclusion? I believe no.
He would reach the conclusion that there could have been a patient above 533 with the same amount of probabilities that there was a patient below 67
Maybe it can be said that there is a bigger chance that a patient was >533 than a patient <67, but not that there MUST have been a patient abot 533
Please correct me, I long forgot my math lessons and I may be mistaken