Normal Distribution Practice

What’s Included

This worksheet contains 20 practice problems organized into four sections:

• Section A: The Empirical Rule (5 problems) — apply the 68-95-99.7 rule to find proportions and ranges for normally distributed data
• Section B: Z-Score Calculations (5 problems) — convert between raw scores and z-scores, compare values across different distributions
• Section C: Normal Probability Calculations (5 problems) — use z-scores and the standard normal table to find probabilities for P(X ≤ x), P(X ≥ x), and P(x₁ ≤ X ≤ x₂)
• Section D: Real-World Applications (5 problems) — apply the normal distribution to test scores, birth weights, manufacturing tolerances, and clinical lab values

An answer key with full solutions is included on the final page.

How to Use

1. Download and print the PDF using the button above
2. Work through each section in order — Sections A and B build skills needed for C and D
3. Use the z-table provided on the worksheet (or the Normal Distribution Calculator)
4. Check your answers against the answer key after completing all problems

Topics Covered

• The empirical rule (68-95-99.7)
• Z-score formula: $z = \frac{x - \mu}{\sigma}$
• Finding probabilities using the standard normal table
• Inverse normal: finding x from a given percentile
• Comparing values across distributions using z-scores
• Real-world contexts: test scores, medical measurements, manufacturing quality

Related

• The Normal Distribution — full tutorial with the empirical rule and z-table
• Z-Scores — calculating and interpreting standard scores
• Normal Distribution Calculator — check your work instantly