Question

A math teacher’s midterm is worth 200 points. The mean of the test is 143 and the standard deviation is 15.7. If the scores have a bell-shaped distribution, what percentage of the scores are between 111.6 and 174.4?

Answer 1

Mean= 143

Standard deviation= 15.7

To find out the percentage of the scores between 111.6 and 174.4, first we need to find out how many SD(Standard deviation) are the values away from the mean. So:

143 - 15.7(x)=111.6

143-111.6=15.7x

31.4=15.7x

x = 31.4 / 15.7

x= 2

So the values are two SD away from the mean.

Then the percentage for two SD away from mean is 95%