Question

bennett middle school has 600 students enrolled in $6^{th}$-$8^{th}$ grades.
a list of 200 students were chosen at random and asked to fill out
a questionnaire regarding any duties they have when they are at home.
the data is shown in the table.

receive allowance	110	90
yard/farm chores	75	125
babysitting duties	45	155
cooking duties	10	190
pet/animal duties	120	80

7 approximately what percent of the population
of bennett middle school can be predicted to have
cooking duties at home?
a 10%
b 5%
c 15%
d 18%

8 about how many middle schoolers at bennett
middle school can be assumed to not receive an
allowance?
a 90
b 270
c 180
d 330

9 if the surveyors predicted 65% of students
would have \house chores\, what was the error of their
prediction in percentage points?
a 12%
b 20%
c 5%
d 14%

10 about how many middle schoolers at
bennett middle school most likely have babysitting
duties?
a 45
b 90
c 29
d 135

Explanation:

Step1: Find sample % for cooking duties

$\frac{10}{200} \times 100\% = 5\%$

Step2: Find non-allowance sample ratio

$\frac{90}{200} = 0.45$; Scale to population: $600 \times 0.45 = 270$

Step3: Calculate actual house chores %

$\frac{140}{200} \times 100\% = 70\%$; Error: $|70\% - 65\%| = 5\%$

Step4: Find babysitting sample ratio

$\frac{45}{200} = 0.225$; Scale to population: $600 \times 0.225 = 135$

Answer:

1. B. 5%
2. B. 270
3. C. 5%
4. D. 135