Question

sat scores the national average for mathematics on a standardized test in 2011 was 510. suppose that the distribution of scores was approximately bell - shaped and that the standard deviation was approximately 46. 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 and

Explanation:

Step1: Recall the empirical rule for normal - distribution

For a normal - distribution (bell - shaped), about 95% of the data lies within 2 standard deviations of the mean.

Step2: Calculate the lower bound

The formula for the lower bound is $\mu - 2\sigma$, where $\mu = 510$ (mean) and $\sigma = 46$ (standard deviation). So, the lower bound is $510-2\times46=510 - 92=418$.

Step3: Calculate the upper bound

The formula for the upper bound is $\mu + 2\sigma$. So, the upper bound is $510+2\times46=510 + 92=602$.

Answer:

418 and 602