a group of 200 college students who took math last term were interviewed. they were asked whether they…

a group of 200 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 | 63 | 21 |\n| live off campus | 43 | 73 |\n(a) what percentage of the students passed math? (%)\n(b) what percentage of the students live on campus? (%)\n(c) what percentage of the students who live on campus passed math? (%)\n(d) is there evidence that students who live on campus tend to pass math more often than average?\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).\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).

a group of 200 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 | 63 | 21 |\n| live off campus | 43 | 73 |\n(a) what percentage of the students passed math? (%)\n(b) what percentage of the students live on campus? (%)\n(c) what percentage of the students who live on campus passed math? (%)\n(d) is there evidence that students who live on campus tend to pass math more often than average?\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).\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).

Answer

Explanation:

Step1: Calculate total students who passed math

Add students who passed math on - campus and off - campus: $63 + 43=106$

Step2: Calculate percentage of students who passed math

Use formula $\text{Percentage}=\frac{\text{Number of students who passed}}{\text{Total number of students}}\times100%$. So $\frac{106}{200}\times100% = 53%$

Step3: Calculate total students who live on campus

Add students who live on campus and passed and failed math: $63+21 = 84$

Step4: Calculate percentage of students who live on campus

Use formula $\text{Percentage}=\frac{\text{Number of students on campus}}{\text{Total number of students}}\times100%$. So $\frac{84}{200}\times100%=42%$

Step5: Calculate percentage of on - campus students who passed math

Use formula $\text{Percentage}=\frac{\text{Number of on - campus students who passed}}{\text{Total number of on - campus students}}\times100%$. So $\frac{63}{84}\times100% = 75%$

Step6: Analyze the evidence

The percentage of all students who passed math is $53%$ (from part (a)), and the percentage of on - campus students who passed math is $75%$ (from part (c)). Since $75%>53%$, there is evidence that students who live on campus tend to pass math more often than average.

Answer:

(a) $53$ (b) $42$ (c) $75$ (d) Yes, because the percentage found in part (c) is much greater than the percentage found in part (a).