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How Hypothesis Tests Are Used in Statistics
Statistical Distributions: Binomial, Normal, and t-Distribution

How z-Values Are Used in Statistics

If a statistical data set has a normal distribution, it is customary to standardize all the data to obtain standard scores known as z-values or z-scores. The distribution of z-values takes on a standard normal distribution (or Z-distribution). The standard normal distribution is a special normal distribution with a mean equal to 0 and a standard deviation equal to 1.

A standard normal (<i>Z-</i>) distribution has a bell-shaped curve with mean 0 and standard deviati
A standard normal (Z-) distribution has a bell-shaped curve with mean 0 and standard deviation 1.

The standard normal distribution is useful for examining the data and determining statistics like percentiles, or the percentage of the data falling between two values. So if researchers determine that the data have a normal distribution, they usually first standardize the data (by converting each data point into a z-value) and then use the standard normal distribution to explore and discuss the data in more detail.

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