transpcr.gif (812 bytes) Standard Deviation

Besides being shifted left or right by the mean, the normal distribution can also be "squeezed" to a narrower shape or "stretched" to a broader shape, relative to the standard normal distribution.

This graph allows you to see how the normal distribution can be squeezed or stretched as the parameter sigma, parameter for standard deviation is changed. For comparison, the standard normal distribution appears in blue.

 
Moving the slider bar changes sigma, parameter for standard deviation, the standard deviation. The mean mu, parameter for the mean is kept constant at 0.
 
If we have a variable Y that has a normal distribution with mean mu, parameter for the mean = 0 and standard deviation sigma, parameter for standard deviation, then we can stretch it or squeeze it so that it has the same distribution as the standard normal distribution by simply dividing by the standard deviation sigma, parameter for standard deviation.    That is,

 z-score denominator

will have the same standard deviation, 1, as the standard normal distribution.

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© 1999, Duxbury Press.