Grade 11 Z-score Worksheet

Z-score Practice Worksheet

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?

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.