Calculate ZScore Using ZStatistic

Using the Z-statistic, calculate the Z-score for a single value $x$ given the mean $\mu$ and standard deviation $\sigma$.

In this problem, you are tasked with calculating the Z-score for a single data point using the Z-statistic formula. This is a foundational concept in statistics, often used to determine how far away a particular data point is from the mean of a data set, in terms of standard deviations. Understanding the Z-score is crucial as it allows you to assess the position of a data point within a distribution, thereby helping in identifying how usual or unusual a particular observation is within the context of the distribution.

A Z-score is a kind of standard score that tells you how many standard deviations an element is from the mean. The Z-score is calculated by subtracting the mean from the value and then dividing by the standard deviation. This method's utility lies in its ability to make different data comparable by standardizing them, which is especially helpful in forming judgments about data drawn from a normal distribution or when comparing results from different data sets or different units.

When solving such problems, it is important to be clear on the dataset's mean and standard deviation, as these are the cornerstone values around which the Z-score revolves. Keep in mind that a high absolute Z-score signifies an element far from the mean, which might be an outlier or have other significance depending on the context and field of study. Recognizing and understanding the application of the Z-score is invaluable in fields ranging from academic research to business analytics, where understanding data positioning within distributions is key to making informed decisions.