Question

a group of 150 college students who took math last term were interviewed. they were asked whether they passed their math course and whether they live on campus. their responses are summarized in the following table.

	passed math	failed math
live off campus	39	21

(a) what percentage of the students passed math? %
(b) what percentage of the students live off campus? %
(c) what percentage of the students who live off campus passed math? %
(d) is there evidence that students who live off campus tend to pass math more often than average?

• yes, because the percentage found in part (c) is much greater than the percentage found in part (a).
• yes, because the percentage found in part (c) is much greater than the percentage found in part (b).
• no, because the percentage found in part (c) is about the same as the percentage found in part (a).
• no, because the percentage found in part (c) is about the same as the percentage found in part (b).

Explanation:

Part (a)

Step1: Find total students who passed math

Students who live on campus and passed: 24; students who live off campus and passed: 39. Total passed = \( 24 + 39 = 63 \).

Step2: Calculate percentage of passed students

Total students = 150. Percentage = \( \frac{63}{150} \times 100 = 42\% \).

Step1: Find total students who live off campus

Students who live off campus: passed (39) + failed (21) = \( 39 + 21 = 60 \).

Step2: Calculate percentage of off - campus students

Percentage = \( \frac{60}{150} \times 100 = 40\% \).

Step1: Identify off - campus and passed students

Off - campus and passed: 39; total off - campus students: 60 (from part b).

Step2: Calculate the percentage

Percentage = \( \frac{39}{60} \times 100 = 65\% \).

Answer:

42

Part (b)