Grade 11 Z-score Worksheet
This worksheet covers Z-score calculations and interpretation for Grade 11 Probability and Statistics.
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Z-score Practice Worksheet
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Read each question carefully and provide your answers in the space provided. Show all your work for calculations.
1. What is the primary purpose of calculating a Z-score?
2. Explain what a positive Z-score indicates about a data point relative to the mean.
3. The formula for calculating a Z-score is Z = (X - μ) / σ, where:
X represents the
μ represents the
σ represents the
4. A set of test scores has a mean of 75 and a standard deviation of 8. Calculate the Z-score for a student who scored 83.
5. In a normal distribution, the average height of adult males is 175 cm with a standard deviation of 7 cm. What is the Z-score for an adult male who is 189 cm tall?
6. A student received a Z-score of -1.5 on a math test. What does this Z-score indicate?
The student scored 1.5 points below the average.
The student scored 1.5 standard deviations below the mean.
The student scored 1.5 standard deviations above the mean.
The student scored 1.5 points above the average.
7. A quality control manager measures the diameter of ball bearings. The mean diameter is 10 mm with a standard deviation of 0.05 mm. Ball bearings with diameters outside of 2 standard deviations from the mean are rejected. What are the minimum and maximum acceptable diameters?
8. Sketch a normal distribution curve. Label the mean (μ), and the points representing ±1, ±2, and ±3 standard deviations from the mean.