They refer to the same thing as do z-transformations.
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The Z-score is just the score. The Z-test uses the Z-score to compare to the critical value. That is then used to establish if the null hypothesis is refused.
no, z score can be negative but a probability is a always positive between 0 and 1.
z-score of a value=(that value minus the mean)/(standard deviation)
It is 84.3%
A negative z score is a value that is less than the mean value.