Final answer:
The question relates to the standard normal distribution in mathematics, specifically in statistics, where z-scores are used to find how many standard deviations a data point is from the mean in a normal distribution with a mean of zero and standard deviation of one.
Step-by-step explanation:
The subject in question, involving a variable z as the standard normal variable, pertains to the concept of the standard normal distribution, which is a key topic in statistics, a branch of mathematics. In the context of the standard normal distribution, z-scores are used to measure the number of standard deviations an individual data point is from the mean. The standard normal distribution is denoted as Z ~ N(0, 1), which means that it is a normal distribution with a mean (μ) of 0 and a standard deviation (σ) of 1.
To calculate the z-score of a data point x from a normal distribution with mean μ and standard deviation σ, the formula is z = (x - μ) / σ. This allows for the comparison of different data points within the same distribution or across different distributions by converting them into a standardized form.
Furthermore, the standard normal distribution is central to various statistical methods, such as hypothesis testing and calculating probabilities for normally distributed random variables.