Question

A certain standardized​ test's math scores have a​ bell-shaped distribution with a mean of 515 and a standard deviation of 105. Complete parts​ (a) through​ (c). ​(a) What percentage of standardized test scores is between 410 and 620​? ​(Round to one decimal place as​ needed.(b) What percentage of standardized test scores is less than 410 or greater than 620​? nothing​% ​(Round to one decimal place as​ needed.) ​(c) What percentage of standardized test scores is greater than 725​? nothing​% ​(Round to one decimal place as​ needed.)

Answer 1

We know by Empirical Rule, for a  bell-shaped distribution

• 68% of data falls within the first standard deviation from the mean.
• 95% fall within two standard deviations.
• 99.7% fall within three standard deviations

(a) As and

So, 68%  of standardized test scores is between 410 and 620.

(b) As the distribution is bell shaped, and by part b) 68%  of standardized test scores is between 410 and 620

Therefore, the percentage of standardized test scores is less than 410 or greater than 620​ is 32%

c) Since,   

and  95% fall within two standard deviations, so greater than 725 , standardized test scores fall.