A set of data items is normally distributed with a mean of 50 and a standard deviation of 8 . Convert 62 to a z-score. \( z_{62}=\square \) (Type an integer or a decimal.)

To convert the value of 62 to a z-score, you subtract the mean from the data point and then divide by the standard deviation. Here’s the formula: \( z = \frac{(X - \mu)}{\sigma} \) Where \( X \) is the value you're converting (62), \( \mu \) is the mean (50), and \( \sigma \) is the standard deviation (8). Plugging in the values: \( z_{62} = \frac{(62 - 50)}{8} = \frac{12}{8} = 1.5 \) So, \( z_{62} = 1.5 \). To understand z-scores better, think of them as your score in a game of statistics! A z-score shows how far away a value is from the average. A positive z-score means it's above the average, while a negative one indicates it's below—just like scoring points over and under your expected performance! Z-scores are not just academic; they have real-world applications! For example, in education, standardized test scores are often converted to z-scores to assess how a student performed relative to peers. This helps educators identify top performers or those needing additional support, ensuring tailored learning experiences and strategies!