Grade 10 Z-score Worksheet
This worksheet helps Grade 10 students understand and calculate Z-scores, and interpret their meaning in a normal distribution.
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Z-score Practice Worksheet
Name:
Date:
Score:
Read each question carefully and show all your work. Use the provided formulas and diagrams to help you answer the questions.
Formula for Z-score: Z = (X - μ) / σ, where X is the data point, μ is the mean, and σ is the standard deviation.
1. In a recent math test, the average score was 75 with a standard deviation of 8. If a student scored 83, what is their Z-score?
2. A student has a Z-score of -1.5 on a science exam. What does this indicate about their performance?
They scored 1.5 standard deviations above the mean.
They scored 1.5 standard deviations below the mean.
They scored exactly the mean.
Their score cannot be determined from the Z-score.
3. In a normal distribution, approximately 68% of the data falls within standard deviation(s) of the mean.
4. A Z-score of 0 means the data point is exactly at the .
5. Sketch a normal distribution curve and label the mean (μ), and the points representing +1, +2, -1, and -2 standard deviations (σ) from the mean.
6. The weights of apples in an orchard are normally distributed with a mean of 180 grams and a standard deviation of 15 grams. An apple weighs 210 grams. Calculate its Z-score and explain what it means.
7. A higher positive Z-score indicates a data point is further above the mean.
True
False
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