Current learning objective: The Standard Normal Distribution Question 18 Prey Score: \( \square \) 0 of 4 points Suppose \( X \sim N(28,2.51) \). Between what \( x \) values does \( 68 \% \) of the data lie? The range of \( x \) values is centered at the mean of the distributionfie., 23). \( 68 \% \) of the data lies between \( \square \) 26 and \( \square \) 30 - (Enter your answers as exact numerical values using the Empirical Rule.)

In the realm of standard normal distribution, the Empirical Rule states that about \(68\%\) of the data falls within one standard deviation of the mean. For your given normal distribution \(X \sim N(28, 2.51)\), the mean is \(28\) and the standard deviation is \(2.51\). Thus, to find the range where \(68\%\) of the data lies, you subtract and add the standard deviation to the mean: \(28 - 2.51 = 25.49\) and \(28 + 2.51 = 30.51\). So the values you’re looking for are approximately \(25.49\) and \(30.51\). In terms of applying this knowledge, understanding the standard normal distribution can be really handy in various fields, like psychology for analyzing test scores, or in healthcare for analyzing patient measurements. Whenever you're working with any normally distributed data, just remember the Empirical Rule (68-95-99.7) and you’ll find a treasure trove of insights in the data! Happy calculating!