Question

Test scores are normally distributed with a mean of 76 and a standard deviation of 10.
a. In a group of 230 tests, how many students score above 96?
b. In a group of 230 tests, how many students score below66?
c. In a group of 230 tests, how many students score within one standard deviation of themean?

Answer 1

For each problem, calculate the z-score and convert it to the appropriate percentile (using a z table or z-score converter), and multiply by the total.

Z-score formula: (value - mean)/(standard deviation)

So for a: we’re calculating for the value 96. The mean is 76, sd is 10. So z-score is (96-76)/10

Convert this to a percentile

Now, since percentiles give you the % below a certain value, and we want the % above that value, we take 100% - the percentile to get the % above 96

Finally, multiply that % by 230 tests

Answer 2

For b) repeat the z score calculation with 66

For c) for a normal distribution, the percentage of values within 1 SD of the mean is 68% so simply calculate 68% of the total values