Question

A study was designed to investigate the effects of two variables - (1) a studentʹs level of mathematical anxiety and (2) teaching method - on a studentʹs 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 470 with a standard deviation of 50 on a standardized test. Assuming no information concerning the shape of the distribution is known, what percentage of the students scored between 370 and 570?

A.approximately 95%

B.at least 75%

C.approximately 68%

D.at least 88.9%

Answer 1

Solution: To find the answer to the given question, we need first find the z score corresponding to x = 370 and x = 570

We are given:

When x = 370, we have:

  

and when x = 570, we have:

  

So we have to find what percentage of data lies within 2 standard deviations from the mean.

We know that the shape of the distribution is unknown. Therefore, using the Chebyshev's inequality, at least 75% of data lies with 2 standard deviation from the mean

So the correct option is B

B. at least 75%