Calculating the survey's relative frequency. Students Seacoast Mountains Totals 7th Grade 60 40 100 8th Grade 90 110 200 Totals 150 150 300 Gloria surveyed all of the campers to determine their preferred field trip. The results are displayed in the table. Which of the following is a relative frequency that can be found with the table? Round the percentage to the nearest tenth.

Question

1. 70% of the people who preferred mountains were 8th graders
2. 40% of the people who preferred the seacoast were 7th graders.
3. 90% of 8th-grade campers preferred the seacoast.
4. 32% of 7th-grade campers preferred the mountains.

Answer 1

To determine the relative frequency of each option based on the survey results given in the table, we will calculate the percentages where applicable.

From the table:

• Total 7th Grade = 100
• Total 8th Grade = 200
• Total students = 300
• Seacoast (total) = 150
• Mountains (total) = 150

1. 70% of the people who preferred mountains were 8th graders.

• Total who preferred mountains = 150
• 8th graders who preferred mountains = 110

Calculating the percentage of mountain-preferring campers who are 8th graders:

\[ \text{Percentage of 8th graders who preferred mountains} = \frac{110}{150} \times 100 = 73.33% \text{ (rounded to 73.3%)} \]

2. 40% of the people who preferred the seacoast were 7th graders.

• Total who preferred seacoast = 150
• 7th graders who preferred seacoast = 60

Calculating the percentage of seacoast-preferring campers who are 7th graders:

\[ \text{Percentage of 7th graders who preferred seacoast} = \frac{60}{150} \times 100 = 40% \]

3. 90% of 8th-grade campers preferred the seacoast.

• Total 8th graders = 200
• 8th graders who preferred seacoast = 90

Calculating the percentage of 8th graders who preferred the seacoast:

\[ \text{Percentage of 8th graders who preferred seacoast} = \frac{90}{200} \times 100 = 45% \]

4. 32% of 7th-grade campers preferred the mountains.

• Total 7th graders = 100
• 7th graders who preferred mountains = 40

Calculating the percentage of 7th graders who preferred mountains:

\[ \text{Percentage of 7th graders who preferred mountains} = \frac{40}{100} \times 100 = 40% \]

Summary of Results:

1. 73.3% (not 70%).
2. 40% (correct).
3. 45% (not 90%).
4. 40% (not 32%).

Conclusion:

The correct relative frequency based on the options is:

2. 40% of the people who preferred the seacoast were 7th graders.