   SEARCH HOME Math Central Quandaries & 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! Paula Paula,

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.

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.