EOC Challenge Set: Statistics and Probability

Use calculator support when helpful, but focus on reading the data carefully and choosing the strongest conclusion the numbers really support.

Practice Set 5

10 EOC-Style Challenge Questions

This set mixes higher-demand table interpretation, expected value, relative performance, variability, dependence, polling, and skewed distribution decisions.

10 questionsEOC challenge

Question 1

Using the table shown, which statement is best supported by the data?

Challenge

Study group	Correct	Not correct	Total
More than 30 minutes	18	6	24
30 minutes or less	10	16	26
Total	28	22	50

Compare the within-group rates before making a claim.

Desmos Move: Compare the percentages within each row, then be careful not to turn association into proof of cause.

Question 2

Game A has expected value $1.20. Game B has expected value $0.40. Which statement is true?

Challenge

Desmos Move: Expected value compares the long-run average outcome, not what must happen in one try.

Question 3

Student A scored 78 on a test with mean 70 and standard deviation 4. Student B scored 88 on a test with mean 80 and standard deviation 10. Who had the stronger relative performance?

Challenge

Desmos Move: Convert both scores to z-scores before comparing the performances.

Question 4

Data Set A has mean 81, median 80, standard deviation 12, and interquartile range 18. Data Set B has mean 81, median 81, standard deviation 5, and interquartile range 6. Which data set is more variable?

Challenge

Desmos Move: Look at both standard deviation and interquartile range. Larger spread measures point to more variability.

Question 5

A box has 3 gold chips and 2 silver chips. Two chips are drawn without replacement. If the first chip is gold, what is the probability that the second chip is silver?

Challenge

Desmos Move: After a gold chip is removed, update both the total number of chips and the number of silver chips left.

Question 6

Which survey is most likely to be biased when estimating the opinion of all students in a school?

Challenge

Desmos Move: Convenience samples tied to one interest group can overrepresent that group's opinion.

Question 7

Scores are approximately normal. About how many of 200 students would be expected to score outside 1 standard deviation of the mean?

Challenge

Numeric response

Desmos Move: If about 68% are within 1 standard deviation, then about 32% are outside that interval.

Question 8

If P(A) = 0.4, P(B) = 0.5, and P(A and B) = 0.2, what can you conclude?

Challenge

Desmos Move: For independent events, the product P(A)P(B) should match P(A and B).

Question 9

Poll A reports 49% support with margin of error 3 points. Poll B reports 52% support with margin of error 4 points. Which statement is most reasonable?

Challenge

Desmos Move: Build both intervals first: 46% to 52% and 48% to 56%.

Question 10

Which measure of center is usually better for a strongly right-skewed income distribution?

Challenge

Desmos Move: Choose the measure that is less affected by extremely large values in the tail.