051. The Standard Error and Normality

If the data in a population are Normally distributed, then the sampling distribution of the sample means will Also be normal.

For Example, there are incomes for several thousand students. These incomes average $500 and they are normally distributed. If all samples of size N are selected from that normal population of student incomes, then the sampling distribution of the sample means will also be normal. This is displayed in Figure 5.2. In Figure 5.2 b, the ’s are more closely clustered around their mean than are individual observations in Figure 5.2 a.

A B

Figure 5.2 – A Normal Distribution: A – Population Distribution;

B –Sampling Distribution

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