Question

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.

	have chores	dont have chores
dont have a curfew	41	39

(a) what percentage of the students have a curfew?
(b) what percentage of the students dont have chores?
(c) what percentage of the students who dont have chores have a curfew?
(d) is there evidence that students who dont have chores tend to have a curfew 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 smaller than the percentage found in part (a)

Explanation:

Step1: Calculate total students with curfew

The number of students with curfew is the sum of those with curfew and chores (24) and those with curfew and no - chores (21). So, $24 + 21=45$.

Step2: Calculate percentage of students with curfew

The total number of students is 125. The percentage of students with curfew is $\frac{45}{125}\times100\%$.
\[

$$\begin{align*} \frac{45}{125}\times100\%&=\frac{45\times100}{125}\%\\ &=\frac{4500}{125}\%\\ & = 36\% \end{align*}$$

\]

Step3: Calculate total students without chores

The number of students without chores is the sum of those without chores and with curfew (21) and those without chores and without curfew (39). So, $21 + 39 = 60$.

Step4: Calculate percentage of students without chores

The percentage of students without chores is $\frac{60}{125}\times100\%$.
\[

$$\begin{align*} \frac{60}{125}\times100\%&=\frac{60\times100}{125}\%\\ &=\frac{6000}{125}\%\\ &=48\% \end{align*}$$

\]

Step5: Calculate percentage of students without chores who have a curfew

The number of students without chores who have a curfew is 21, and the number of students without chores is 60. The percentage is $\frac{21}{60}\times100\%$.
\[

$$\begin{align*} \frac{21}{60}\times100\%&=\frac{21\times100}{60}\%\\ &=\frac{2100}{60}\%\\ & = 35\% \end{align*}$$

\]

Step6: Analyze if students without chores tend to have a curfew more often than average

The percentage of all students with a curfew is 36% (from part a), and the percentage of students without chores who have a curfew 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)