Algebra 2 Normal Distribution Quiz – Free PDF

Contents

This algebra 2 normal distribution quiz asks 10 multiple-choice questions on data, normal distributions and statistical inference, and each answer comes with a short explanation.

Ten multiple-choice questions check the main ideas: standard deviation, the 68-95-99.7 rule, z-scores, study design and margin of error. Pick the one best answer for each question, then read the explanation to see the typical mistake.

Algebra 2Common Core: S-ID.A.4 · S-IC.A.1 · S-IC.B.3 · S-IC.B.4

🎯 Data, Normal Distributions and Statistical Inference – Algebra 2 math quiz

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Question 1

Values are approximately normal with mean 60 and standard deviation 5. What percent of values lie between 55 and 65?

Mean 60, standard deviation 5.

A \(68\%\)

B \(34\%\)

C \(95\%\)

D \(50\%\)

Question 2

A student scores 92 on a test with mean 80 and standard deviation 8. What is the z-score?

A \(z=12\)

B \(z=0.67\)

C \(z=-1.5\)

D \(z=1.5\)

Question 3

Every value in a data set with mean 20 and standard deviation 4 is increased by 10. What are the new mean and standard deviation?

A mean 30, SD 4

B mean 30, SD 14

C mean 20, SD 14

D mean 30, SD 40

Question 4

About what percent of a normal distribution with mean 500 and standard deviation 50 lies in the shaded region above 600?

Mean 500, standard deviation 50; the tail above 600 is shaded.

A \(2.5\%\)

B \(5\%\)

C \(13.5\%\)

D \(16\%\)

Question 5

Researchers randomly assign 50 patients to take either a new medicine or a placebo and compare recovery times. What kind of study is this?

A a sample survey

B an experiment

C an observational study

D a census

Question 6

A study finds that students who eat breakfast have higher grades. The students chose whether to eat breakfast. Which conclusion is justified?

A Eating breakfast causes higher grades.

B Eating breakfast is associated with higher grades.

C Skipping breakfast lowers grades.

D Every student should eat breakfast.

Question 7

A poll reports that 54% of voters support a measure, with a margin of error of 4 percentage points. Which statement is best supported?

A Exactly 54% of all voters support it.

B The poll proves that most voters support it.

C At most 4% of voters oppose the measure.

D The true percent is plausibly from 50% to 58%.

Question 8

A teacher wants to survey 40 of her 800 students. Which method gives a random sample?

A Survey the first 40 students who enter the cafeteria.

B Survey the 40 members of the chess club.

C Number all students and pick 40 numbers with a random number generator.

D Survey the 40 students who answer an online post.

Question 9

The histogram shows 200 simulated sample percents. The shaded bars, the middle 95% of results, run from 31% to 50%. What is the estimated margin of error?

200 simulated samples of 100 people.

A about 19 percentage points

B about 40 percentage points

C about 4.75 percentage points

D about 9.5 percentage points

Question 10

Why do researchers use random assignment in an experiment?

A It guarantees that the results apply to a whole population.

B It makes the sample size larger so the margin of error is zero.

C It makes the groups comparable so differences can be credited to the treatment.

D It lets participants choose the treatment they prefer.

🎉 Quiz complete!

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How does this quiz work?

Read each question, choose one answer among A, B, C and D, then check it: a short explanation appears after every answer. Your score out of 10 is shown at the end, and you can restart the quiz as often as you like.

What should you review before the quiz?

Reread the key facts of the lesson and the worked example. If a question is hard, go back to the matching part of the lesson, then try the quiz again. Write your work on scrap paper: most mistakes come from skipping a step, not from the idea itself.

Remember:

Standards S-ID.A.4, S-IC.A.1, S-IC.B.3 and S-IC.B.4: normal models, z-scores, study design and margin of error.
Normal data follow the 68-95-99.7 rule: \(68\%\), \(95\%\) and \(99.7\%\) within 1, 2 and 3 standard deviations.
The z-score is \(z=\frac{x-\mu}{\sigma}\); the table gives the area to the left of \(z\).
Only an experiment with random assignment can support a cause-and-effect conclusion.
A margin of error can be estimated as half the width of the middle \(95\%\) of simulated sample results.