Question

A study was designed to investigate the effects of two variables N (1) a student's level of mathematical anxiety and (2) teaching method N 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 400 with a standard deviation of 40 on a standardized test. Assuming no information concerning the shape of the distribution is known, what percentage of the students scored between 320 and 480?

A) approximately 95%

B) approximately 68%

C) at least 75%

D) at least 89%

Answer 1

Solution :

Given that ,

mean = = 400

standard deviation = = 40

P(320 < x < 480) = P[(320 - 400)/ 40) < (x - ) /  < (480 - 400) / 40) ]

= P(-2.0 < z < 2.0)

= P(z < 2.0) - P(z < -2.0)

Using z table,

= 0.9772 - 0.0228

= 0.9544

percentage = approximately = 95%