Z-score Analysis Worksheet
A Grade 12 Math worksheet focusing on Z-score calculations and interpretation in probability and statistics.
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Z-score Analysis Worksheet
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Date:
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Read each question carefully and provide your answers in the space provided. Show all your work for calculations.
1. A Z-score measures how many an element is from the mean.
2. A positive Z-score indicates the data point is the mean, while a negative Z-score indicates it is the mean.
3. The formula for calculating a Z-score is Z = (x - μ) / .
4. Explain the significance of a Z-score of 0.
5. In a normal distribution with a mean of 50 and a standard deviation of 10, what is the Z-score for a value of 65?
-1.5
0.5
1.5
2.0
6. Which of the following statements about Z-scores is true?
A Z-score always has a positive value.
Z-scores are used to compare scores from different normal distributions.
The mean of a set of Z-scores is always 1.
A high Z-score always indicates a better performance.
7. A student scored 88 on a math test where the class average was 82 and the standard deviation was 4. Another student scored 75 on a science test where the class average was 70 and the standard deviation was 3. On which test did the student perform relatively better? Justify your answer using Z-scores.
8. The diagram below represents a standard normal distribution curve. Label the mean (μ) and the points corresponding to Z-scores of -1, 0, and 1.
9. A Z-score of -2.5 indicates that a data point is 2.5 standard deviations below the mean.
True
False