The z-score is given by \( z=\frac{x-\mu}{\sigma} \). Find the \( z \)-score rounded to three decimal places if \( x=1.772, \mu=3.781 \), and \( \sigma=2.744 \). The z-score is \( z=\frac{1.772-3.781}{2.744}= \)

To find the z-score, we first substitute the values into the formula: \( z = \frac{1.772 - 3.781}{2.744} \). Calculating the numerator: \( 1.772 - 3.781 = -2.009 \). Now, divide this by \( 2.744 \): \( z = \frac{-2.009}{2.744} \approx -0.731 \). So, rounding to three decimal places, the z-score is \( z \approx -0.731 \). The z-score is a nifty way to understand how far and in what direction a particular data point differs from the mean of a distribution. In our case, with a z-score of approximately -0.731, it indicates that the value of 1.772 is about 0.731 standard deviations below the mean of 3.781. You can find z-scores in a multitude of real-world scenarios! For example, in academic performance, students’ scores can be converted into z-scores to see how individual performance ranks in relation to the class average. A higher z-score, for instance, means you’re acing it compared to your peers!