DOK 2 Practice Set: Statistics and Probability Connections

Use Desmos tables, lists, and quick calculations while you connect conditional probability, expected value, z-scores, and distribution comparisons.

Practice Set 2

10 Connected Questions

This set focuses on multi-step probability, independence, expected value, z-scores, normal distribution estimates, sampling, and comparing distributions.

10 questionsDOK 2 review

Question 1

Using the two-way table shown, what is the conditional probability that a student passed given that the student used the review guide?

DOK 2

Group	Passed	Did not pass	Total
Used review guide	24	6	30
Did not use guide	12	18	30
Total	36	24	60

Decide whether the condition is about guide use or passing before you pick the correct total.

Desmos Move: The condition tells you which row or column becomes the new total for the probability.

Question 2

Based on the same table, are passing the quiz and using the review guide independent events?

DOK 2

Desmos Move: Compare the conditional probability to the overall probability of passing.

Question 3

A game has a 0.25 chance of winning $8 and a 0.75 chance of winning $2. It costs $3 to play. What is the expected net value?

DOK 2

Numeric response

Desmos Move: Compute the expected prize first, then subtract the cost, or use the net outcomes directly.

Question 4

A test score of 78 comes from a distribution with mean 70 and standard deviation 4. What is the z-score?

DOK 2

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

Question 5

School A and School B both have mean score 82 on a benchmark. School A has standard deviation 4 and School B has standard deviation 9. Which school has the more consistent scores?

DOK 2

Desmos Move: Consistency means a tighter cluster around the mean, so look for the smaller standard deviation.

Question 6

Scores are approximately normal with mean 70 and standard deviation 5. About how many of 200 students would you expect to score between 65 and 75?

DOK 2

Numeric response

Desmos Move: The interval from 65 to 75 is within 1 standard deviation of the mean, so use the 68% benchmark.

Question 7

A poll says that 54% of students prefer digital notes with a margin of error of 3 percentage points. Which interval matches the poll result?

DOK 2

Desmos Move: Move the estimate down and up by 3 percentage points.

Question 8

Which sample is most likely to be biased if a school wants to estimate how all students feel about homework length?

DOK 2

Desmos Move: Ask whether everyone in the population had a fair chance to be selected.

Question 9

Using the summary table shown, which data set has the larger interquartile range?

DOK 2

Data set	Q1	Median	Q3
A	72	80	88
B	76	81	84

Interquartile range compares the middle 50% of the data.

Desmos Move: Compute interquartile range as Q3 minus Q1 for each data set.

Question 10

Using the study table, what is the conditional probability that a student used the review guide given that the student passed?

DOK 2

Group	Passed	Did not pass	Total
Used review guide	24	6	30
Did not use guide	12	18	30
Total	36	24	60

Decide whether the condition is about guide use or passing before you pick the correct total.

Desmos Move: The condition changes in this question. Now the total must come from the students who passed.