Math CentralQuandaries & Queries


Anita, a student:

A variable Y has a distribution of mean of Y =80 and standard deviation of Y=36. Find the values of A and B for transforming y*=A +BY so that mean of y* =0 and standard deviation of y*=1.

Hi Anita,

What you are trying to find is standard normal distribution where mean is 0 and the standard deviation is 1. We can convert any normally distributed population to standard normal distribution using z-scores.

The z- score is z = (x-μ)/σ where
x is a raw score to be standardized
σ is the standard deviation of the population
μ is the mean of the population.

For example: Find the z-score corresponding to a raw score of 132 from a normal distribution with mean 100 and standard deviation 15.

z = (132-100)/15 = 32/15= 2.133

Our new raw score is 2.133.

Hope this helps,


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