THE NORMAL DISTRIBUTION

The most important continuous probability distribution in the field of statistics is the normal distribution :

1. empirical data is often normally, or approximately normally, distributed
2. the assumption of normality allows for the application of powerful statistical analyses
3. the distribution of many sample statistics tends to normality as the sample size increases (>30)
4. many population distributions can be readily transformed to normality

The properties of the normal distribution are :

1. observations tend to cluster at the mean:  mean = mode = median
2. the distribution of observations is symmetrical about the vertical axis through the mean
3. the total area under the curve is equal to unity, i.e. 1.0000
4. the normal curve continues to decrease in height as one proceeds in either direction away from the mean, but never reaches the horizontal axis, i.e. there is a presumption of negative and positive infinity
5. the area under the curve between two ordinates, X = a and X = b where a < b, represents the probability that X lies between a and b and can be expressed by the probability of a < X < b
6. when the variable X is expressed in standard units, z = (X - m)/@

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