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What kind of distribution is a standard z distribution?
It is the normalised Gaussian distribution. To speak of a 'standard z' distribution is somewhat redundant because a z-score is already standardised. A z-score follows a normal or Gaussian distribution with a mean of zero and a standard deviation of one. It's these specific parameters (this mean and standard deviation) that are considered 'standard'. Speaking of a z-score implies a standard normal distribution. This is important because the shape of the normal distribution remains the same no matter what the mean or standard deviation are. As a consequence, tables of probabilities and other kinds of data can be calculated for the standard normal and then used for other variations of the distribution.
When do you use a z - table compared with when you use a t - table?
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.
What percentage of the area of a normal standard distribution falls between z and z?
Zero.
What is the shape of a z-score distribution?
The standard normal distribution or the Gaussian distribution with mean 0 and variance 1.
What is the z-values associated with the middle 44 percent of the standard normal distribution?
-0.772 < Z < 0.772
