Hello Mathematicians!(adsbygoogle = window.adsbygoogle || []).push({});

I'm doing some work on obtaining true measures of ability for students, and am trying to find a simple mathematical example that would show that a student's true ability is obtained by having a few equally weighted tests rather than one big test.

The example I'm thinking of is something along the lines of:

A student's "true" ability is 70/100, but if they sit an exam there will be a slight error in their ability measurement. Say that their mark will be normally distributed with a mean of 70 and a standard deviation of 5. So there is a 68% chance that their mark is between 65 and 75.

Now rather than sit a single exam, say that they sit 2 exams instead - both of which their mark will come from a normal distribution with mean 70 and standard deviation 5. The exams will be equally weighted as 50% of their total mark.

Now earlier, if they sat a single exam, there would be a 68% chance that their mark would be between 65 and 75. Now that they are sitting 2 exams each weighted at 50%, what would the probability be that their total mark is between 65 and 75?

Also, what about if there were 3 exams of equal weighting, etc.?

Thanks for the help guys.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Question regarding probability and normal distributions.

**Physics Forums | Science Articles, Homework Help, Discussion**