Use Chebyshev s Inequality to Describe Any Set of Data
-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 350 with a standard deviation of 20 on a standardized test. Assuming no information concerning the shape of the distribution is known, what percentage of the students scored between 310 and 390
A) at least $75 \%$
B) approximately 95\%
C) at least $88.9 \%$
D) approximately $68 \%$

Question

Use Chebyshev s Inequality to Describe Any Set of Data
-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 350 with a standard deviation of 20 on a standardized test. Assuming no information concerning the shape of the distribution is known, what percentage of the students scored between 310 and 390 
A) at least $75 \%$
B) approximately 95\%
C) at least $88.9 \%$
D) approximately $68 \%$

Quizplus · Accepted Answer

Chebyshev's Inequality states that for any distribution, the proportion of observations within k standard deviations of the mean is at least $1 - \frac{1}{k^2}$. Here, $k = \frac{390 - 350}{20} = 2$ for the upper bound and $k = \frac{350 - 310}{20} = 2$ for the lower bound. Thus, at least $1 - \frac{1}{2^2} = 1 - \frac{1}{4} = \frac{3}{4} = 75\%$ of the students scored between 310 and 390.

Use Chebyshev S Inequality to Describe Any Set of Data 75%75 \%75%

Use Chebyshev S Inequality to Describe Any Set of Data $75 \%$