Standard Normal Distribution

The normal distribution curve, as mentioned in Chapter 15, occupies a preeminent position in statistics. That the frequency distributions of many (though not necessarily all) natural and man-made random variables approximate to this shape is an important reason for its significance, which is further enhanced, as we have seen, by the consequence of the Central Limit Theo­rem. This significance, in turn, is derived from the mathematical relation to which the normal distribution curve conforms, mean­-ing that the x-y relation of this curve is entirely determined by two statistics: (1) the mean μx,, and (2) the standard deviation, σx, both of which are either known or can be determined from the given set of variables. In other words, a given normal distri­bution is a function of these two variables, and the shape of that distribution curve is unique; thus, two or more normal distribu­tions having the same means, μx, and the same standard devia­tion, σx, are totally identical.

Source: Srinagesh K (2005), The Principles of Experimental Research, Butterworth-Heinemann; 1st edition.