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To answer these questions, let's analyze the given information and calculate the required values step-by-step.
### (a) What percentage of the students have a curfew?
We start by identifying the total number of students who have a curfew. This includes students who have both a curfew and chores, as well as those who have a curfew but no chores.
- Students with curfew and chores: 37
- Students with curfew but no chores: 33
The total number of students with a curfew is:
[tex]\[ 37 + 33 = 70 \][/tex]
Next, we calculate the percentage of students with a curfew:
[tex]\[ \left( \frac{70}{125} \right) \times 100 = 56\% \][/tex]
So, 56% of the students have a curfew.
### (b) What percentage of the students don't have chores?
We identify the total number of students who do not have chores. This includes both those who have a curfew and those who don’t have a curfew.
- Students with curfew but no chores: 33
- Students with no curfew and no chores: 27
The total number of students without chores is:
[tex]\[ 33 + 27 = 60 \][/tex]
Next, we calculate the percentage of students without chores:
[tex]\[ \left( \frac{60}{125} \right) \times 100 = 48\% \][/tex]
So, 48% of the students don't have chores.
### (c) What percentage of the students who don't have chores have a curfew?
We need to determine the percentage of students without chores who have a curfew.
- Students without chores who have a curfew: 33
- Total students without chores: 60
The percentage is calculated as follows:
[tex]\[ \left( \frac{33}{60} \right) \times 100 = 55\% \][/tex]
So, 55% of the students who don't have chores have a curfew.
### (d) Is there evidence that students who don't have chores tend to have a curfew more often than average?
To determine this, we compare the percentage of students who don't have chores and have a curfew (55%) with the overall percentage of students who have a curfew (56%) and the percentage of students who don't have chores (48%).
Given the comparisons:
1. The percentage of students who have a curfew is 56%.
2. The percentage of students who don't have chores is 48%.
3. The percentage of students who don't have chores and have a curfew is 55%.
We see that 55% is very close to the overall percentage of students with a curfew (56%) but is considerably higher than the percentage of students without chores (48%).
Hence, the correct conclusion is:
Yes, because the percentage found in part (c) is much greater than the percentage found in part (b).
Therefore, the evidence suggests that students who don't have chores tend to have a curfew more often than those who do, based on the comparison of the relevant percentages.
### (a) What percentage of the students have a curfew?
We start by identifying the total number of students who have a curfew. This includes students who have both a curfew and chores, as well as those who have a curfew but no chores.
- Students with curfew and chores: 37
- Students with curfew but no chores: 33
The total number of students with a curfew is:
[tex]\[ 37 + 33 = 70 \][/tex]
Next, we calculate the percentage of students with a curfew:
[tex]\[ \left( \frac{70}{125} \right) \times 100 = 56\% \][/tex]
So, 56% of the students have a curfew.
### (b) What percentage of the students don't have chores?
We identify the total number of students who do not have chores. This includes both those who have a curfew and those who don’t have a curfew.
- Students with curfew but no chores: 33
- Students with no curfew and no chores: 27
The total number of students without chores is:
[tex]\[ 33 + 27 = 60 \][/tex]
Next, we calculate the percentage of students without chores:
[tex]\[ \left( \frac{60}{125} \right) \times 100 = 48\% \][/tex]
So, 48% of the students don't have chores.
### (c) What percentage of the students who don't have chores have a curfew?
We need to determine the percentage of students without chores who have a curfew.
- Students without chores who have a curfew: 33
- Total students without chores: 60
The percentage is calculated as follows:
[tex]\[ \left( \frac{33}{60} \right) \times 100 = 55\% \][/tex]
So, 55% of the students who don't have chores have a curfew.
### (d) Is there evidence that students who don't have chores tend to have a curfew more often than average?
To determine this, we compare the percentage of students who don't have chores and have a curfew (55%) with the overall percentage of students who have a curfew (56%) and the percentage of students who don't have chores (48%).
Given the comparisons:
1. The percentage of students who have a curfew is 56%.
2. The percentage of students who don't have chores is 48%.
3. The percentage of students who don't have chores and have a curfew is 55%.
We see that 55% is very close to the overall percentage of students with a curfew (56%) but is considerably higher than the percentage of students without chores (48%).
Hence, the correct conclusion is:
Yes, because the percentage found in part (c) is much greater than the percentage found in part (b).
Therefore, the evidence suggests that students who don't have chores tend to have a curfew more often than those who do, based on the comparison of the relevant percentages.
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