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Suppose a student just found out that she scored a 75 on her first statistics​ exam, with a​ z-score of 0.5. Her​ friend, who is in a different section with the same​ professor, also scored a 75 but had a​ z-score of −0.5. What can you conclude about the mean exam scores in the two​ classes?

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Answer:

The mean exam scores in the second section is greater than the mean exam scores in the first section

Step-by-step explanation:

Here, we are interested in making a conclusion.

Mathematically;

z-score = (score - mean)/SD

so basically, what determines the sign of the z-score is dependent entirely on the mean.

If the mean is larger than the score, we will have a negative z-score. If the mean is smaller than the score, then will have a positive z-score

So basically what drives the sign is the mean value since the scores are the same for both students in this case, irrespective of the standard deviation in both classes.

So, for the first girl with a positive z-score, we can conclude that her score is larger than the mean; while for the second girl with a negative z-score, her score is smaller to the mean.

Thus, what we conclude here is that the mean score of the second section with the professor is greater than the mean score of the first section with the professor.