Practice Set 6
10 Readiness Questions
This set reviews conditional probability, independence, expected value, z-scores, standard deviation, normal distribution estimates, sampling, and margin of error.
Practice Questions
Mixed Readiness Check: Statistics and Probability
Use this final set to check whether you can read conditions carefully, compare spread, and interpret survey language without getting rushed.
Question 1
Using the table shown, what is the conditional probability that a student passed given that the student listens to music while studying?
| Group | Passed | Did not pass | Total |
|---|---|---|---|
| Listens to music | 14 | 6 | 20 |
| No music | 12 | 18 | 30 |
| Total | 26 | 24 | 50 |
Read the condition carefully before choosing the total for the probability.
Desmos Move: The phrase given that tells you which group becomes the total for the probability.
Question 2
A fair coin is flipped, recorded, and flipped again. Are the two flips independent?
Desmos Move: Ask whether the first outcome changes the probability of the second outcome.
Question 3
A game costs $3. You win $20 with probability 0.1 and $0 otherwise. What is the expected net value?
Desmos Move: Use the net outcomes of +17 dollars and -3 dollars when you calculate the average result.
Question 4
What does a z-score of -1 tell you about a data value?
Desmos Move: The sign shows direction from the mean, and the number shows how many standard deviations away the value is.
Question 5
Which sample of five values is likely to have the larger standard deviation?
Desmos Move: The larger standard deviation comes from the set that spreads farther away from its center.
Question 6
Scores are approximately normal. About how many of 300 students would be expected to score above 1 standard deviation above the mean?
Desmos Move: About 16% of a normal distribution lies above 1 standard deviation above the mean.
Question 7
Two data sets have the same median. Data Set A has interquartile range 6 and Data Set B has interquartile range 14. Which set has more spread in the middle 50%?
Desmos Move: Interquartile range directly measures the spread of the middle 50% of the data.
Question 8
Which sampling method is best described as random?
Desmos Move: A random start with a full roster helps avoid convenience sampling.
Question 9
A poll estimate is 61% with a margin of error of 4 percentage points. What does that margin of error suggest?
Desmos Move: Margin of error creates an interval around the estimate instead of a single guaranteed value.
Question 10
Which tool is most useful for organizing the relationship between two categorical variables?
Desmos Move: Categorical-versus-categorical relationships are often organized with counts in rows and columns.