Which is better, a score of 92 on a test with a mean of 71 and a standard deviation of 15, or a score of 688 on a test with a mean of 493 and a standard deviation of 150?

a. Both scores have the same relative position
b. A score of 92
c. A score of 688

The z-score for a score of 92 is higher than the z-score of a score of 688, therefore, the score that is better is: b. A score of 92

Recall:

Z-score for a score of 92:

raw score = 92

mean = 71

standard deviation = 15

Z-score = (92 - 71)/15 = 1.4

Z-score for a score of 688:

raw score = 688

mean = 493

standard deviation = 150

Z-score = (688 - 493)/150 = 1.3

Therefore, the z-score for a score of 92 is higher than the z-score of a score of 688, therefore, the score that is better is: b. A score of 92

Learn more about z-score on:

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b. A score of 92

Step-by-step explanation:

The z-score measures how many standard deviations a score is above or below the mean.

It is given by the following formula:

In which is the score, is the mean and is the standard deviation.

In this problem, we have that:

The best score is the one with a higher z-score. If the z-score is the same for both, then they have the same relative position.

A score of 92 on a test with a mean of 71 and a standard deviation of 15.

Here we have

So

A score of 688 on a test with a mean of 493 and a standard deviation of 150

Here we have

The score of 92 has a higher Z-score, so it is better.

The correct answer is:

b. A score of 92

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