Respuesta :
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 = [tex]\frac{X-\mu}{\sigma}[/tex] ; where, [tex]\mu[/tex] = mean
[tex]\sigma[/tex] = standard deviation
For 1st situation; z score = [tex]\frac{82-70}{8}[/tex] = 1.50
For 2nd situation; z score = [tex]\frac{82-75}{4}[/tex] = 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.
