Algebra 2 Normal Distribution and Z-scores Test

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

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Looking for a normal distribution and z-scores test? Then this Algebra 2 test on Normal Curves, z-Scores and Study Design checks the whole chapter, with points for each question. This 45-minute test covers standard deviation, z-scores, the Empirical Rule, study design and margin of error from a simulation. A calculator is allowed. Show your reasoning in each question.

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

Time: 45 minutes · 9 questions · Total: 20 points · Calculator: as allowed by your teacher

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Question 1 Mean and standard deviation (2 points)

Find the mean and the population standard deviation of 3, 7, 8, 10, 12. Round σ to the nearest hundredth.

Question 2 z-scores (2 points)

A distribution has mean 52 and standard deviation 4.5. Find the z-score of 61, and the value that has z-score −0.8.

Question 3 Heights and the Empirical Rule (3 points)

Adult heights in a town are approximately normal with mean 66 inches and standard deviation 2.5 inches.

Figure for Question 3.

What percent of adults are between 61 and 71 inches? (1 point)
What percent are shorter than 63.5 inches? (1 point)
What percent are taller than 71 inches? (1 point)

Question 4 Compare swimmers (3 points)

In the 100-meter freestyle, last season’s boys’ times had mean 60 seconds and standard deviation 1.5 seconds, and the girls’ times had mean 52 seconds and standard deviation 1 second. Jo (boys) swam 58.2 seconds and Lee (girls) swam 50.5 seconds. Who did better relative to their group? A lower time is better.

Question 5 Classify the study (2 points)

Classify each study as a survey, an observational study or an experiment. (a) A gym randomly assigns 40 members to two workout plans and compares fitness gains. (b) A town clerk records the ages of everyone who attends a council meeting.

Question 6 Margin of error from a histogram (3 points)

A class simulated 100 random samples of 30 people from a population where half agree with a statement. The histogram shows the sample proportions.

Figure for Question 6.

Estimate the interval holding the middle 95% of the results. (2 points)
Estimate the margin of error. (1 point)

Question 7 Counting students above a score (2 points)

Scores on a statewide test are approximately normal with mean 70 and standard deviation 8. About how many of 400 students scored above 78?

Question 8 Identify bias (2 points)

A principal surveys only students who stay after school for clubs to find out how students get to school. Explain the bias and suggest a better sampling plan.

Question 9 Cause and effect (1 point)

Which design can show that a new fertilizer causes taller plants: a survey or a randomized experiment? Why?

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