Normal Distribution and Z-scores Quiz – Algebra 2 (10 Questions)

Last updated: October 22, 2026 · Written by the Math Made Easy math teachers

Standards: S-ID.A.4, S-IC.A.1, S-IC.B.3, S-IC.B.4 · Level: Grade 11 Algebra 2

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What this Normal Curves, z-Scores and Study Design quiz checks

• σ is the square root of the average squared deviation from the mean.
• Empirical Rule: 68%, 95% and 99.7% within 1, 2 and 3 standard deviations.
• z = (x − μ)/σ; |z| greater than 2 marks an unusual value.
• Only a randomized experiment can support a cause-and-effect conclusion.
• Simulating many random samples shows the margin of error: about twice the standard deviation of the sample proportions.

The 10 questions of the quiz

1. What does a z-score measure?
2. A value is 2 standard deviations above the mean. What is its z-score?
3. In a normal distribution, about what percent lie within 2 standard deviations of the mean?
4. Mean 100 and σ = 15. About what percent of values are between 85 and 115?
5. Scores: mean 50, σ = 10. What is the z-score of 35?
6. Which study design can establish cause and effect?
7. Which sample is most likely to be unbiased?
8. A simulation of 100 samples gives the histogram. The middle 95% runs from about 0.48 to 0.70. The margin of error is about
9. The data set 9, 9, 9, 9, 9 has a standard deviation of
10. Test A: mean 70, σ = 5, score 80. Test B: mean 60, σ = 10, score 75. Which score is better relative to its test?

After the quiz

Missed a question? Reread the Normal Curves, z-Scores and Study Design lesson, then take the quiz again. Next, solve the Algebra 2 worksheet on Normal Curves, z-Scores and Study Design, one star first, then two and three stars. Finally, take the chapter test under real conditions, without notes and with a timer.

Mis à jour le 22 October 2026