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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?

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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.
User Greg Sansom
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3 votes

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)

User Vinod Vishwanath
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8.2k points