Question

a group of 220 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.

	live on campus	live off campus
failed math	22	77

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

Explanation:

Step1: Calculate percentage of students who passed math

The total number of students is \(66 + 22+55 + 77=220\). The number of students who passed math is \(66 + 55=121\). The percentage of students who passed math is \(\frac{121}{220}\times100 = 55\%\)

Step2: Calculate percentage of students who live on - campus

The number of students who live on - campus is \(66+22 = 88\). The percentage of students who live on - campus is \(\frac{88}{220}\times100=40\%\)

Step3: Calculate percentage of on - campus students who passed math

The number of on - campus students who passed math is \(66\). The number of on - campus students is \(88\). The percentage of on - campus students who passed math is \(\frac{66}{88}\times100 = 75\%\)

Step4: Analyze evidence

The percentage of all students who passed math is \(55\%\), and the percentage of on - campus students who passed math is \(75\%\). Since \(75\%>55\%\), there is evidence that students who live on campus tend to pass math more often than average.

Answer:

(a) 55%
(b) 40%
(c) 75%
(d) Yes, because the percentage found in part (c) is much greater than the percentage found in part (a).