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 what is the value of x in the relative frequency table for the survey results? round the answer to the nearest percent. art classes oil painting sculpture total satisfied 34% 84%

Explanation:

Step1: Calculate total number of students surveyed

The number of students in oil - painting is \(17 + 3=20\), and in sculpture is \(25 + 5 = 30\). So the total number of students surveyed is \(20+30=50\).

Step2: Calculate the number of satisfied students

The number of satisfied students is \(17 + 25=42\).

Step3: Calculate the relative frequency of satisfied students in sculpture

The relative frequency of satisfied students in sculpture is \(\frac{25}{50}\times100\% = 50\%\).

Step4: Calculate the value of \(x\)

The sum of relative - frequencies of satisfied students in oil - painting and sculpture should equal the total relative frequency of satisfied students. Let the relative frequency of satisfied students in sculpture be \(y\). We know that \(34\%+y = 84\%\), so \(y=84\% - 34\%=50\%\). The total number of students is \(50\). The number of students in sculpture is \(30\). The number of satisfied students in sculpture is \(25\). The relative frequency of satisfied students in sculpture is \(\frac{25}{50}\times100\% = 50\%\). We are not using this to find \(x\). To find \(x\), we first note that the total number of students is \(50\). The number of students who are not satisfied in oil - painting is \(3\). The relative frequency of students who are not satisfied in oil - painting is \(\frac{3}{50}\times100\%=6\%\).

Answer:

6%