DOK 3 Practice Set: Statistics and Probability Reasoning

Use Desmos and careful reading to evaluate claims, compare data fairly, and decide what conclusions the numbers actually support.

Practice Set 3

10 Strategic Questions

This set focuses on survey bias, cause-versus-association reasoning, z-score comparisons, expected value decisions, and evaluating what data can really prove.

10 questionsDOK 3 review

Question 1

A school surveys only after-school club members about whether buses should leave later. Why should the results be used carefully?

DOK 3

Desmos Move: Check whether the sampling method gives all parts of the population a fair chance to be represented.

Question 2

Using the two-way table shown, which conclusion is best supported by the data?

DOK 3

Group	High score	Not high score	Total
Tutoring	18	6	24
No tutoring	12	14	26
Total	30	20	50

Compare percentages within each group before making a conclusion.

Desmos Move: Compare percentages, then separate association from cause-and-effect language.

Question 3

Class A has mean 84 and standard deviation 2. Class B has mean 88 and standard deviation 11. A student wants scores that stay close to the class average instead of swinging widely. Which class looks more consistent?

DOK 3

Desmos Move: A smaller standard deviation means scores stay closer to the mean, even if the mean itself is lower.

Question 4

Student A scored 78 on a test with mean 70 and standard deviation 4. Student B scored 84 on a test with mean 80 and standard deviation 10. Who performed better relative to the group?

DOK 3

Desmos Move: Compare z-scores instead of raw scores when the tests have different means and standard deviations.

Question 5

Game A gives a net gain of $9 with probability 0.2 and a net loss of $1 with probability 0.8. Game B gives a net gain of $4 with probability 0.5 and a net loss of $1 with probability 0.5. Which game has the greater expected value?

DOK 3

Desmos Move: Compute each expected value separately before comparing the games.

Question 6

Poll 1 estimates 52% support with a margin of error of 4 percentage points. Poll 2 estimates 47% support with a margin of error of 3 percentage points. What conclusion is most reasonable?

DOK 3

Desmos Move: Write both intervals first, then see whether they overlap before making a strong claim.

Question 7

A score of 62 comes from a distribution with mean 50 and standard deviation 5. What is the z-score?

DOK 3

Numeric response

Desmos Move: Subtract the mean from the score, then divide by the standard deviation.

Question 8

A bag contains 4 blue chips and 3 green chips. Two chips are drawn without replacement. Are the events independent or dependent?

DOK 3

Desmos Move: Without replacement means the first draw changes what is left for the second draw.

Question 9

Which data display is especially useful for spotting possible outliers quickly?

DOK 3

Desmos Move: Think about which display separates the middle data from extreme values clearly.

Question 10

Using the tutoring table, what is the strongest correct statement?

DOK 3

Group	High score	Not high score	Total
Tutoring	18	6	24
No tutoring	12	14	26
Total	30	20	50

Compare percentages within each group before making a conclusion.

Desmos Move: Compare the rates within each row instead of comparing only the raw counts.