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In my study, I inject a different amount of fluid in each experiment, such as 1 ml, 2 ml..., and test the change in the general dielectric properties of the solution.

Now that I have done much (over 100) measurements for each injection in a specific volume, one can see that for each injection the values of the new dielectric properties have a normal distribution with specified mean and variance.

For example: for injection of 1 ml, the results distribute with μ1 and σ1, for injection of 2 ml we get μ2 and σ2. When there is some overlap between the various distributions.

Now suppose I get an X value of dielectric property, what is the correct way to estimate the probability that the value X came from a specific injection volume?

Seemingly, I could use the Z test for each distribution separately, but it seems to me that the Z test does not take into account the other distributions.

Thank you!