Question

mr. capuano, an art teacher, surveyed his students to find out whether they are satisfied with his classes. he also noted which class each student had taken.
oil painting
satisfied: 17
not satisfied: 3
sculpture
satisfied: 25
not satisfied: 5
art classes
table with columns: oil painting, sculpture, total; rows: satisfied (34%, blank, 84%), ... (partially visible)
what is the value of x in the relative frequency table for the survey results? round the answer to the nearest percent.
options: ○ 3% ○ 6% ○ 8% ○ 15%

Explanation:

Step1: Find total number of students

First, calculate the total number of students from the Oil Painting class. In Oil Painting, satisfied is 17 and not satisfied is 3, so total for Oil Painting is \(17 + 3 = 20\). The relative frequency for satisfied in Oil Painting is 34%, let total students be \(T\). So \(0.34=\frac{17}{T}\), solving for \(T\) gives \(T=\frac{17}{0.34}=50\).

Step2: Find number of satisfied in Sculpture

Total satisfied students: 84% of 50 is \(0.84\times50 = 42\). Satisfied in Oil Painting is 17, so satisfied in Sculpture is \(42 - 17 = 25\) (which matches the given data, good check).

Step3: Find relative frequency of not satisfied in Oil Painting (x)

Number of not satisfied in Oil Painting is 3. Total students is 50. So relative frequency \(x=\frac{3}{50}\times100 = 6\%\).

Answer:

6% (Option: 6%)