Math CentralQuandaries & Queries


Good afternoon,

I am hoping that you may be able to help me with a question in which I am finding myself stumped. I am so pleased that I have found your website - it's full of great information and very helpful tips. I have included my question below:

Consider a data set that is normally distributed. The mean of the data set is equal to 10,000.

a.) Suppose that, for this data set, 10,625 has a "z-value" = 2.5. Solve for the standard deviation of the data set.

b.) Solve for the "z-value" of 9,900.

Thank you so much for your help and consideration!



If X is a normal random variable with mean μ and variance σ and Z is the standard normal random variable then Z = (X - μ)/σ.

You know that μ = 10,000 and when X = 10,625 then Z = 2.5. Substitute into the expression above and solve for the standard deviation σ. Now that you know σ you can convert X = 9,900 to its Z-value.


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