z score, also called z value, normal score, or standard score, is the standardized value of a normal random variable. The difference between the value of an observation and the mean of the distribution is usually called the deviation from the mean of the observation. The z score is then a dimensionless quantity obtained by dividing the deviation from the mean of the observation by the standard deviation of the distribution. In the following, random variables are represented by uppercase letters such as X and Z, and the specific values of the random variable are represented by the corresponding lowercase letters such as x and z.
The normal distribution is a family of normal random variables. A normal random variable X with ...
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