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 1 of 2 (a) within what boundaries would you expect 95% of the scores to fall? about 95% of the scores should fall between 418 and 602. part: 1 / 2 part 2 of 2 (b) what percentage of scores would be above 648? % of the scores would be above 648.

Explanation:

Step1: Calculate the z - score

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value, $\mu$ is the mean and $\sigma$ is the standard deviation. Given $\mu = 510$, $\sigma=46$ and $x = 648$. Then $z=\frac{648 - 510}{46}=\frac{138}{46}=3$.

Step2: Use the standard normal distribution properties

The total area under the standard - normal curve is 1. The area to the left of $z = 3$ from the standard normal table is approximately 0.9987. The area to the right of $z = 3$ (the percentage of scores above 648) is $1-0.9987 = 0.0013$. To convert this to a percentage, we multiply by 100. So the percentage is $0.13\%$.

Answer:

$0.13$