A study was designed to investigate the effects of two variables long dash ​(1) a​ student's level of mathematical anxiety and​ (2) teaching method long dash on a​ student's achievement in a mathematics course. Students who had a low level of mathematical anxiety were taught using the traditional expository method. These students obtained a mean score of 250 with a standard deviation of 40 on a standardized test. Assuming a​ mound-shaped and symmetric​ distribution, in what range would approximately 99.7​% of the students​ score?

Accepted Solution

99.7% of the students would fall between 130 and 370.

Using the empirical rule we know that 99.7% of the data falls within 3 standard deviations of the mean.  The standard deviation is 120, so this means our range is from 250-120 to 250+120, or 130 to 370.