Converting Z-Scores into Actual Scores (HSC SSCE Mathematics Standard): Quizzes

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Converting Z-Scores into Actual Scores
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What is the formula for converting a z-score into an actual score?

x=xˉ+z×sx = \bar{x} + z \times s

In the formula x=xˉ+z×sx = \bar{x} + z \times s, what does xˉ\bar{x} represent?

Mean of the data set

If mean is 3030, SD is 3.53.5, and z-score is 22, what is the actual score?

3737

If mean is 3434, SD is 44, and z-score is 1.5-1.5, what is the actual score?

2828

What does a positive z-score indicate about the actual score?

Score is above the mean

What does a negative z-score indicate about the actual score?

Score is below the mean

In the formula x=xˉ+z×sx = \bar{x} + z \times s, what does ss represent?

Standard deviation

If z-score is positive, how should the actual score compare to the mean?

Actual score should be greater than mean

Which method is usually quicker for converting z-scores?

Using direct formula x=xˉ+z×sx = \bar{x} + z \times s

If mean is 71.571.5, SD is 6.46.4, z-score is 2.52.5, what is the actual score (nearest whole)?

8888

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