Question

Which score has the highest relative position: a score of 38 on a test with a mean of 30 and a standard deviation of 10, a score of 4.2 on a test with a mean of and a standard deviation of or a score of 432 on a test with a mean of and a standard deviation of (Assume that the distributions being compared have approximately the same shape.)

Answer 1

A score of 4.2 on a test with a mean of 2.5 and a standard deviation of 1.2 has the highest relative position.

Explanation:

Which score has the highest relative position: a score of 38 on a test with a mean of 30 and a standard deviation of 10, a score of 4.2 on a test with a mean of 2.5 and a standard deviation of 1.2 or a score of 432 on a test with a mean of 396 and a standard deviation of 40.

In order to find the solution, we need to calculate the z score value for each test.

The z score formula:
`z = \frac{\bar{x} -\mu}{s}` where
`\bar{x}` is the score, μ is the mean and s is the standard deviation.

Now for test 1:

Put
`\bar{x}=38, \mu=30 \text{ and } s=10` in the above formula.

`z = (38 -30)/(10)`

`z = 0.8`

For test 2:

Put
`\bar{x}=4.2, \mu=2.5 \text{ and } s=1.2` in the above formula.

`z = (4.2 -2.5)/(1.2)`

`z \approx 1.417`

For test 3:

Put
`\bar{x}=432, \mu=396 \text{ and } s=40` in the above formula.

`z = (432 -396)/(40)`

`z =0.9`

Since the z score value of test 2 is greater so a score of 4.2 on a test with a mean of 2.5 and a standard deviation of 1.2 has a highest relative position.