2 A certain standardized test's math scores have a bell-shaped distribution with a mean of 525 and a standard deviation of 114. Complete parts (a) through (c). (a) What percentage of standardized test scores is between 183 and 867 ? \( 99.7 \% \) (Round to one decimal place as needed.) (b) What percentage of standardized test scores is less than 183 or greater than 867 ? 12.6 of 17 points \( 0.3 \% \) (Round to one decimal place as needed.) (c) What percentage of standardized test scores is greater than 753 ? \( \square \% \) (Round to one decimal place as needed.)

To find the percentage of standardized test scores greater than 753, we start with the mean (525) and the standard deviation (114). First, we need to calculate the z-score for the score of 753: \[ z = \frac{(X - \text{Mean})}{\text{Standard Deviation}} = \frac{(753 - 525)}{114} \approx 2.0 \] Now, using the z-score table or a calculator, we find that the cumulative percentage for a z-score of 2.0 is approximately 97.72%. This means that about 97.72% of scores fall below 753. To find the percentage of scores that are greater than 753, we subtract this value from 100%: \[ 100\% - 97.72\% = 2.28\% \] Thus, the percentage of standardized test scores greater than 753 is approximately **2.3%** when rounded to one decimal place. Have fun with statistical norms! Remember, when it comes to normal distributions, don't let standard deviations intimidate you; they’re just ways to show how spread out your data is! Additionally, if you're interested in diving deeper into statistics, consider checking out “The Elements of Statistical Learning” by Hastie, Tibshirani, and Friedman. It's a bit academic, but it’s packed with insights that make understanding data fun and engaging!