Practice Set 1
10 Foundational Questions
This set focuses on two-way tables, conditional probability basics, expected value, standard deviation, z-scores, normal distribution benchmarks, and margin of error.
Practice Questions
DOK 1 Practice Set: Statistics and Probability Foundations
Use Desmos tables or quick calculator checks while you review vocabulary, read two-way tables, and interpret core distribution ideas.
Question 1
In the two-way table shown, how many students both play a sport and have a pet?
| Group | Has pet | No pet | Total |
|---|---|---|---|
| Plays sport | 18 | 12 | 30 |
| Does not play sport | 10 | 20 | 30 |
| Total | 28 | 32 | 60 |
Use inside cells for joint counts and row or column totals for conditional probabilities.
Desmos Move: Read the row and column labels first so you match the correct cell instead of using a total by mistake.
Question 2
Using the same table, what is the conditional probability that a student has a pet given that the student plays a sport?
| Group | Has pet | No pet | Total |
|---|---|---|---|
| Plays sport | 18 | 12 | 30 |
| Does not play sport | 10 | 20 | 30 |
| Total | 28 | 32 | 60 |
Use inside cells for joint counts and row or column totals for conditional probabilities.
Desmos Move: For a conditional probability, use only the row or column named after the condition as the total.
Question 3
Based on the same table, are playing a sport and having a pet independent events?
Desmos Move: Compare the conditional probability to the overall probability. If they differ, the events are not independent.
Question 4
A game costs $2 to play. You win $10 with probability 0.25 and $0 otherwise. What is the expected net value?
Desmos Move: Use the net outcomes, not just the prize values. The two net results are +8 dollars and -2 dollars.
Question 5
Two quiz score distributions have the same mean. One has a standard deviation of 12 and the other has a standard deviation of 4. Which distribution has more spread?
Desmos Move: Larger standard deviation means the data values are typically farther from the mean.
Question 6
What does a z-score of 0 mean for a data value?
Desmos Move: A z-score measures distance from the mean in standard deviation units, so a z-score of 0 means no distance at all.
Question 7
In an approximately normal distribution, about what percent of the data lies within 1 standard deviation of the mean?
Desmos Move: Use the common 68-95 rule for normal distributions.
Question 8
Class A and Class B have the same mean test score. Class A has standard deviation 2 and Class B has standard deviation 7. Which class has more consistent scores?
Desmos Move: More consistent means the scores stay closer to the mean, which matches the smaller standard deviation.
Question 9
A survey reports that 62% of students prefer digital notes with a margin of error of 3 percentage points. Which interval best matches that report?
Desmos Move: Margin of error means move the estimate up and down by the reported number of percentage points.
Question 10
Which data display is especially helpful for comparing medians, quartiles, and possible outliers?
Desmos Move: Think about which display is built from the five-number summary.