a group of 125 students were asked whether they have a curfew and whether they have chores at home. their…

a group of 125 students were asked whether they have a curfew and whether they have chores at home. their responses are summarized in the following table.\n| |have chores|dont have chores|\n|--|--|--|\n|have a curfew|24|21|\n|dont have a curfew|41|39|\n(a) what percentage of the students have a curfew? (%)\n(b) what percentage of the students dont have chores? (%)\n(c) what percentage of the students who dont have chores have a curfew? (%)\n(d) is there evidence that students who dont have chores tend to have a curfew 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 125 students were asked whether they have a curfew and whether they have chores at home. their responses are summarized in the following table.\n| |have chores|dont have chores|\n|--|--|--|\n|have a curfew|24|21|\n|dont have a curfew|41|39|\n(a) what percentage of the students have a curfew? (%)\n(b) what percentage of the students dont have chores? (%)\n(c) what percentage of the students who dont have chores have a curfew? (%)\n(d) is there evidence that students who dont have chores tend to have a curfew 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 percentage of students with curfew

The number of students with curfew is $24 + 21=45$. The total number of students is $125$. The percentage formula is $\frac{\text{Number of students with curfew}}{\text{Total number of students}}\times100%$. So, $\frac{45}{125}\times 100%=\frac{4500}{125}=36%$.

Step2: Calculate percentage of students without chores

The number of students without chores is $21 + 39 = 60$. Using the percentage formula $\frac{\text{Number of students without chores}}{\text{Total number of students}}\times100%$, we get $\frac{60}{125}\times100%=\frac{6000}{125}=48%$.

Step3: Calculate percentage of students without chores who have curfew

The number of students without chores who have curfew is $21$. The number of students without chores is $60$. Using the percentage formula $\frac{\text{Number of students without chores who have curfew}}{\text{Number of students without chores}}\times100%$, we have $\frac{21}{60}\times100%=\frac{2100}{60}=35%$.

Step4: Analyze the relationship

The percentage of students with curfew (from part a) is $36%$, and the percentage of students without chores who have curfew (from part c) is $35%$. Since these percentages are about the same, there is no evidence that students who don't have chores tend to have a curfew more often than average.

Answer:

(a) $36$ (b) $48$ (c) $35$ (d) No, because the percentage found in part (c) is about the same as the percentage found in part (a).