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How can you find X with just the mean and standard deviation? Is it possible, or do you need a z score as well? If it's possible could you show me the formula and an example?

Typically you will need the z-score as well as the mean and standard deviation to find a particular X (data point.)

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Suppose you are given an ordered list of 10 numbers. The arithmetic mean of those numbers is given by `mu=bar(x)=(sum_(i=1)^n x_(i))/n` where n=10 and `x_i` is the ith data point. (The numbers need not be sorted, but you need to know the first entry, second entry, etc...)

If instead I told you that the mean of 10 data points was 5.5 and the sum of 9 of the data points was 48, you could find the remaining data point. (The sum of all 10 is 55 since the mean is 5.5 so the missing point is 55-48=7.) Here we can find an "X" with the mean and the sum of all of the data points except X. Note that the standard deviation was not...

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