mr. capuano, an art teacher, surveyed his students to find out whether they are satisfied with his classes…

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. 3% 6% 8% 15% art classes\n| | oil painting | sculpture | total |\n|--|--|--|--| \n| satisfied | 34% | | 84% |

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. 3% 6% 8% 15% art classes\n| | oil painting | sculpture | total |\n|--|--|--|--| \n| satisfied | 34% | | 84% |

Answer

Explanation:

Step1: Calculate total number of students in oil - painting

The number of satisfied students in oil - painting is 17 and not - satisfied is 3. So the total number of students in oil - painting is $17 + 3=20$.

Step2: Calculate total number of students surveyed

Let the total number of students surveyed be $N$. Since the relative frequency of satisfied students in oil - painting is 34% and the number of satisfied students in oil - painting is 17, we have $\frac{17}{N}=0.34$. Solving for $N$, we get $N=\frac{17}{0.34}=50$.

Step3: Calculate number of satisfied students in sculpture

The relative frequency of satisfied students in total is 84%, so the number of satisfied students in total is $0.84\times50 = 42$. Since the number of satisfied students in oil - painting is 17, the number of satisfied students in sculpture is $42−17 = 25$.

Step4: Calculate number of students in sculpture

The number of satisfied students in sculpture is 25 and not - satisfied is 5, so the total number of students in sculpture is $25 + 5=30$.

Step5: Calculate relative frequency of satisfied students in sculpture

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

Step6: Calculate $x$

The sum of relative frequencies of satisfied students in oil - painting and sculpture should be 84%. Let the relative frequency of satisfied students in sculpture be $y$. We know $34%+y = 84%$, so $y = 50%$. The relative frequency of not - satisfied students in sculpture is $\frac{5}{50}\times100% = 10%$. The relative frequency of not - satisfied students in oil - painting is $\frac{3}{50}\times100%=6%$. So $x = 6%$.

Answer:

6%