The sample should not be normally distributed.
If you have a population of size N from which a random sample of size n is to be drawn, then there are NCn possible samples. Each one of these must have the same probability of being thesample. That is, the sample is uniformly distributed - not Normally.
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The Z test.
The mean and standard deviation. If the data really are normally distributed, all other statistics are redundant.
You use the central limit theorem when you are performing statistical calculations and are assuming the data is normally distributed. In many cases, this assumption can be made provided the sample size is large enough.
no
The means of repeated samples from any population.