Practice Set 4
10 Mixed Questions
This set blends two-way tables, independence, expected value, spread, skew, z-scores, normal distributions, and sampling.
Practice Questions
Mixed Practice Set A: Statistics and Probability Review
Use quick Desmos checks and careful reading while you move between conditional probability, expected value, normal distributions, and survey ideas.
Question 1
A two-way table shows 21 students both attended a review session and passed a benchmark. What kind of count is 21?
Desmos Move: Inside cells of a two-way table show counts that belong to both categories at the same time.
Question 2
If 21 of the 30 students who attended the review session passed, what is the conditional probability of passing given attendance?
Desmos Move: Use the group named in the condition as the total.
Question 3
A bag has 5 red tiles and 5 blue tiles. A tile is drawn, recorded, replaced, and the bag is mixed before the next draw. Are the two draws independent?
Desmos Move: Replacement resets the bag, so the second draw keeps the same probabilities as the first draw.
Question 4
A game costs $1. You win $4 with probability 0.5 and $0 with probability 0.5. What is the expected net value?
Desmos Move: Use the net outcomes of +3 dollars and -1 dollar, then weight them by probability.
Question 5
Which set of scores is likely to have the larger standard deviation?
Desmos Move: The more spread out the values are from the center, the larger the standard deviation tends to be.
Question 6
If a distribution is skewed right, which relationship is often true?
Desmos Move: A long right tail pulls the mean farther to the right than the median.
Question 7
A score of 90 comes from a distribution with mean 80 and standard deviation 5. What is the z-score?
Desmos Move: The score is 10 above the mean, and each standard deviation is worth 5 points.
Question 8
In an approximately normal distribution, about what percent of the data lies within 2 standard deviations of the mean?
Desmos Move: Use the second benchmark in the usual normal distribution rule.
Question 9
A survey reports that 48% of students prefer paper notes with a margin of error of 2 percentage points. Which interval is correct?
Desmos Move: Margin of error means go down and up by the stated number of percentage points.
Question 10
Which sampling method is most likely to produce a random sample of all students in a school?
Desmos Move: A good random sample starts from the whole population and gives each student a fair chance to be selected.