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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.)

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Answer:

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.

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