Which sampling method is most likely to give a representative sample of a school's 800 students?
A. Asking students in one fifth-grade class
B. Surveying students who stay after school for chess club
C. Choosing every tenth name from an alphabetical list of all students
D. Asking only students who volunteer
Show answer and reasoning
Correct answer: C. Choosing every tenth name from an alphabetical list of all students
Systematic selection from the full list gives every student a fair chance of inclusion.
- A: One class does not represent all grades.
- B: Chess club members are a self-selected group.
- D: Volunteers may differ systematically from other students.
Source: CSET MS Mathematics SMR 4.2 Inferences, Predictions, and Arguments Based on Data
A box plot of quiz scores shows a minimum of 60, first quartile 70, median 80, third quartile 90, and maximum 100. What percent of scores are at or above 80?
A. 50 percent
B. 75 percent
C. 25 percent
D. 100 percent
Show answer and reasoning
Correct answer: A. 50 percent
The median splits the data in half, so about 50 percent are at or above 80.
- B: 75 percent are at or above the first quartile (70).
- C: 25 percent are above the third quartile.
- D: Only scores at or above 60 make up 100 percent.
Source: CSET MS Mathematics SMR 4.2 Inferences, Predictions, and Arguments Based on Data
A bag holds 3 red, 5 blue, and 2 green marbles. What is the probability of drawing a blue marble?
A. 1/2
B. 1/5
C. 3/10
D. 5/5
Show answer and reasoning
Correct answer: A. 1/2
5 blue out of 10 marbles = 5/10 = 1/2.
- B: 1/5 is the probability of green.
- C: 3/10 is the probability of red.
- D: 5/5 equals 1, which would mean certainty.
Source: CSET MS Mathematics SMR 4.3 Basic Notions of Chance and Probability
A fair coin is flipped twice. What is the probability of getting heads both times?
Show answer and reasoning
Correct answer: B. 1/4
The flips are independent: 1/2 x 1/2 = 1/4.
- A: 3/4 is the probability of at least one tail.
- C: 1/3 does not correspond to any outcome with two equally likely flips.
- D: 1/2 is the probability of heads on a single flip.
Source: CSET MS Mathematics SMR 4.3 Basic Notions of Chance and Probability
A standard six-sided die is rolled. What is the probability of rolling a number greater than 4?
Show answer and reasoning
Correct answer: D. 1/3
The outcomes 5 and 6 satisfy the condition: 2/6 = 1/3.
- A: 2/3 is the probability of rolling greater than 2.
- B: 1/6 is the probability of a single specific number.
- C: 1/2 would require three favorable outcomes.
Source: CSET MS Mathematics SMR 4.3 Basic Notions of Chance and Probability
