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.

(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?

o no, because the percentage found in part (c) is about the same as the percentage found in part (a).

o no, because the percentage found in part (c) is about the same as the percentage found in part (b).

o yes, because the percentage found in part (c) is much greater than the percentage found in part (a).

Explanation:

Step1: Calculate percentage of students passed math

Total students = \(22 + 66+77 + 55=220\)
Students passed math \(=66 + 55 = 121\)
Percentage \(=\frac{121}{220}\times100=\frac{12100}{220}=55\%\)

Step2: Calculate percentage of students live on campus

Students live on campus \(=22+66 = 88\)
Percentage \(=\frac{88}{220}\times100=\frac{8800}{220}=40\%\)

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

Students who live on campus and passed math \(=66\)
Percentage \(=\frac{66}{88}\times100=\frac{6600}{88}=75\%\)

Step4: Calculate percentage of students who live off - campus passed math

Students who live off - campus \(=77 + 55=132\)
Students who live off - campus and passed math \(=55\)
Percentage \(=\frac{55}{132}\times100=\frac{5500}{132}\approx41.67\%\)

Since \(75\%>41.67\%\), 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).