Is there a way to aggregate multiple Z-scores to get a single Z-score that corresponds to the probability that no null hypotheses are rejected?
Backstory: We have a tool that has some error E that it adds to each measurement. Assume E is normally distributed with mean 0 and standard deviation 1. Given multiple readings from the tool, I want to find the Z-score that corresponds to the probability that none of the true values exceed a certain threshold T.
Let's assume that the error in each measurement is independent.
EDIT: Here is an example. Suppose I have a slightly imperfect scale where the difference (in lbs) between the reported and true weights follows a standard normal distribution.
I weigh 3 objects and get readings of 1,2, and 3 lbs. What is the likelihood that at least one of the objects weighs 4 or more lbs?
Is there a way to solve this question with only a single Z-score lookup at the end?