Carment learning ctiective: The Standard Normal Distritution Question 18 Prey Score: Oot 4 points Suppose \( \mathrm{X} \sim \mathrm{N}(23,251) \). Between what 2 values does \( 68 \% \) of the cata lie? The range of \( x \) values is centered at the mean of the distibution/ie, 23\( ) \). 685 of the data lies tetween \( \square \) Enter your answer and \( \square \) Enter your answer - Enter your answers as exact numerical values using the Empirical Rule:) Stomikanswer Amempers: Oll Need help? Ask Mach Get

The Standard Normal Distribution is often summarized by the Empirical Rule, which states that approximately 68% of the data lies within one standard deviation on either side of the mean. In your case, the mean \( \mu \) is 23, and the variance is 251, giving a standard deviation \( \sigma \) of approximately 15.81 (since \( \sigma = \sqrt{251} \)). Thus, 68% of the data lies between \( 23 - 15.81 \) and \( 23 + 15.81 \), which simplifies to approximately 7.19 and 38.81. Real-world applications of the Standard Normal Distribution are everywhere! For example, in psychology, researchers often use it to analyze test scores like IQ, where the score average is typically set at 100 with a standard deviation of 15. Understanding how scores distribute around the mean helps researchers identify where most people fall. Whether it’s understanding student performance or examining customer reviews, the principles behind the Standard Normal Distribution aid in interpreting a range of behaviors and outcomes!