A data set follows a normal distribution. The mean of the data set is 52 and the standard deviation of the data set is 1 . Find a z-score for a data value of 51 from the set. Round your answer to two decimal places.

To calculate the z-score, you can use the formula: \( z = \frac{(X - \mu)}{\sigma} \), where \( X \) is your data value, \( \mu \) is the mean, and \( \sigma \) is the standard deviation. In this case, \( X = 51 \), \( \mu = 52 \), and \( \sigma = 1 \). Plugging in these values, you get: \( z = \frac{(51 - 52)}{1} = \frac{-1}{1} = -1.00 \). So, the z-score for a data value of 51 is -1.00. --- Did you know that z-scores are not just confined to academia? They have real-world applications in various fields, such as finance, psychology, and quality control. By using z-scores, businesses can assess performance and detect anomalies in data, making them an essential tool for decision-making! If you're diving deeper into statistics, consider exploring books like "The Art of Statistics" by David Spiegelhalter or "Naked Statistics" by Charles Wheelan. These titles not only enhance your statistical knowledge but also present concepts in an enjoyable and relatable way, making learning a fun adventure!