a group of 175 college students who took math last term were interviewed. they were asked whether they…

a group of 175 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.\n| | passed math | failed math |\n|--|--|--| \n| live on campus | 28 | 77 |\n| live off campus | 49 | 21 |\n(a) what percentage of the students passed math? (%)\n(b) what percentage of the students live off campus? (%)\n(c) what percentage of the students who live off campus passed math? (%)\n(d) is there evidence that students who live off campus tend to pass math more often than average?\nyes, because the percentage found in part (c) is much greater than the percentage found in part (a).\nyes, because the percentage found in part (c) is much greater than the percentage found in part (b).\nno, because the percentage found in part (c) is about the same as the percentage found in part (a).\nno, because the percentage found in part (c) is about the same as the percentage found in part (b).

a group of 175 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.\n| | passed math | failed math |\n|--|--|--| \n| live on campus | 28 | 77 |\n| live off campus | 49 | 21 |\n(a) what percentage of the students passed math? (%)\n(b) what percentage of the students live off campus? (%)\n(c) what percentage of the students who live off campus passed math? (%)\n(d) is there evidence that students who live off campus tend to pass math more often than average?\nyes, because the percentage found in part (c) is much greater than the percentage found in part (a).\nyes, because the percentage found in part (c) is much greater than the percentage found in part (b).\nno, because the percentage found in part (c) is about the same as the percentage found in part (a).\nno, because the percentage found in part (c) is about the same as the percentage found in part (b).

Answer

Explanation:

Step1: Calculate total students

The total number of students is 175.

Step2: Calculate percentage of students who passed math

The number of students who passed math is (28 + 49=77). The percentage is (\frac{77}{175}\times100%). [ \begin{align*} \frac{77}{175}\times100%&=\frac{77\times100}{175}%\ &=\frac{7700}{175}%\ & = 44% \end{align*} ]

Step3: Calculate percentage of students who live off - campus

The number of students who live off - campus is (49 + 21 = 70). The percentage is (\frac{70}{175}\times100%). [ \begin{align*} \frac{70}{175}\times100%&=\frac{70\times100}{175}%\ &=\frac{7000}{175}%\ &=40% \end{align*} ]

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

The number of students who live off - campus and passed math is 49. The percentage is (\frac{49}{70}\times100%). [ \begin{align*} \frac{49}{70}\times100%&=\frac{49\times100}{70}%\ &=\frac{4900}{70}%\ & = 70% \end{align*} ]

Step5: Analyze part (d)

The percentage of students who passed math overall is 44% (from part (a)), and the percentage of students who live off - campus and passed math is 70%. Since 70% is much greater than 44%, students who live off - campus tend to pass math more often than average.

Answer:

(a) 44 (b) 40 (c) 70 (d) Yes, because the percentage found in part (c) is much greater than the percentage found in part (a).