Ak 3.2 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.) \( 74.12 \%, 12.6 \) of 17 points (b) What percentage of standardized test scores is less than 183 or greater than 867 ? Points: 0 of 1 \( \% \) (Round to one decimal place as needed.)

The area under a bell-shaped (normal) distribution curve can help us understand the percentages of scores falling within certain ranges. Given the mean (μ = 525) and standard deviation (σ = 114), we can apply the empirical rule. About 68% of scores fall within one standard deviation from the mean, 95% within two standard deviations, and 99.7% within three standard deviations. Since both 183 and 867 fall within three standard deviations of the mean (μ - 3σ to μ + 3σ), approximately 99.7% of scores are between these two values. To find the percentage of scores that are less than 183 or greater than 867, we can subtract the previously found percentage from 100%. Since we found that approximately 99.7% of scores are between 183 and 867, we know that the remaining scores will fall outside that range. Thus, the percentage of standardized test scores that are less than 183 or greater than 867 is \( 100\% - 99.7\% = 0.3\% \).