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A study was designed to investigate the effects of two variables​(1) a​ student's level of mathematical anxiety and​ (2) teaching methodon 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 440 with a standard deviation of on a standardized test. Assuming no information concerning the shape of the distribution is​ known, what percentage of the students scored between 360 and 520 ​?

Respuesta :

Using Chebyshev's Theorem, considering a standard deviation of 40, we have that at least 75% of the students scored between 360 and 520.

What does Chebyshev’s Theorem state?

When we have no information about the population distribution, Chebyshev's Theorem is used. It states that:

  • At least 75% of the measures are within 2 standard deviations of the mean.
  • At least 89% of the measures are within 3 standard deviations of the mean.
  • An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].

In this problem, considering a standard deviation of 40, we have that:

440 - 2 x 40 = 360.

440 + 2 x 30 = 520.

Within 2 standard deviations of the mean, no information about the distribution, hence, at least 75% of the students scored between 360 and 520.

More can be learned about Chebyshev's Theorem at https://brainly.com/question/25303620

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