Determine the lower boundary for 95% of the scores: SAT Scores The national average for mathematics on a standardized test in 2011 was 511 . Suppose that the distribution of scores was approximately bellshaped and that the standard deviation was approximately 41 . Round your answers to at least one decimal place as needed. Part: $0 / 2$ Part 1 of 2 (a) Within what boundaries would you expect $95 \%$ of the scores to fall? About $95 \%$ of the scores should fall between $\square$ and $\square$.

Step 1 ：The problem is asking for the boundaries within which 95% of the scores would fall. This is a statistics problem that involves the concept of normal distribution. In a normal distribution, 95% of the data falls within 2 standard deviations of the mean.

Step 2 ：To find the boundaries, we need to calculate the mean plus and minus 2 times the standard deviation. The mean is given as 511 and the standard deviation is given as 41.

Step 3 ：Calculate the lower boundary: mean - 2 * std_dev = 511 - 2 * 41 = 429

Step 4 ：Calculate the upper boundary: mean + 2 * std_dev = 511 + 2 * 41 = 593

Step 5 ：Final Answer: About 95% of the scores should fall between \( \boxed{429} \) and \( \boxed{593} \)