Question

Which is better: 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?

Answer 1

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 = $\frac{X-\mu}{\sigma}$ ; where, $\mu$ = mean

                                                                              $\sigma$ = standard deviation

For 1st situation; z score = $\frac{82-70}{8}$ = 1.50

For 2nd situation; z score = $\frac{82-75}{4}$ = 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.