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Frequency Distribution Table
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For statistical tests based on (Student's) t-distribution you use the t-table. This is appropriate for small sample sizes - up to around 30. For larger samples (or degrees of freedom), the t-distribution becomes very close to the Standard Normal distribution so you use the z-tables.
Yes.
The z-score table is the cumulative distribution for the Standard Normal Distribution. In real life very many random variables can be modelled, at least approximately, by the Normal (or Gaussian) distribution. It will have its own mean and variance but the Z transform converts it into a standard Normal distribution (mean = 0, variance = 1). The Z-distribution is then used to make statistical inferences about the data. However, there is no simple analytical method to calculate the values of the distribution function. So, it has been done and tabulated for easy reference.