Question

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?

Answer 1

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.

Answer 2

Answer:
`(130,\ 370)`

Explanation:

Given : Sample Mean score :
`\overline{x}=250`

Standard deviation :
`\sigma=40`

The range that would represent the approximately 99.7​% of the students​ score :-

`\overline{x}\pm 3\sigma`

i.e.
`250\pm 3(40)/tex]</p><p>i.e. [tex]250\pm 120/tex]</p><p>[tex]=(250-120,\ 250+120)=(130,\ 370)`

Hence, the range that represents the approximately 99.7​% of the students​ score =
`(130,\ 370)`