Answer:
A score of 82 on a test with a mean of 75 and a standard deviation of 4 is better.
Step-by-step explanation:
We are given two situations;
A score of 82 on a test with a mean of 70 and a standard deviation of 8 or
A score of 82 on a test with a mean of 75 and a standard deviation of 4.
Now, we have to find which is better. For this we will calculate z score for both the situations;
The z score value is given by, Z = ; where,
= mean
= standard deviation
For 1st situation; z score = = 1.50
For 2nd situation; z score = = 1.75
So, it is clear that 2nd situation is better as it has higher z score.
Therefore, a score of 82 on a test with a mean of 75 and a standard deviation of 4 is better.