A study was designed to investigate the effects of two variables - (1) a student's level of mathematical anxiety and (2) teaching method - 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 390 with a standard deviation of 30 on a standardized test. Assuming a non-mound-shaped distribution, what percentage of the students scored over 480?
A) at most 11%
B) at least 89%
C) approximately 2.5%
D) at most 5.5%

Question

Quizplus · Accepted Answer

The non-mound-shaped distribution means that the data is not normally distributed. Therefore, we cannot use the normal distribution to calculate the percentage of students who scored over 480. However, we can use the Chebyshev's theorem to calculate the minimum percentage of students who scored over 480. Chebyshev's theorem states that for any data set, at least 1 - 1/k^2 of the data will fall within k standard deviations of the mean. In this case, k = (480 - 390) / 30 = 3. Therefore, at least 1 - 1/3^2 = 89% of the students scored over 480.

A Study Was Designed to Investigate the Effects of Two