Use the table to answer the question.

Question

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.

(1 point)
Responses

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

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

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

40% of the people who preferred the seacoast were 7th graders.
40% of the people who preferred the seacoast were 7th graders.
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Answer 1

To find the correct relative frequency, we will calculate the necessary values based on the information in the table.

1. Relative Frequency of 7th Graders who preferred the Mountains:
   • There are 40 students who preferred the Mountains in 7th Grade.
   • Total number of 7th Graders = 100.
   • Relative Frequency = (Number of 7th Graders who preferred Mountains) / (Total 7th Graders) = 40 / 100 = 0.40 or 40%.

So, the statement "32% of 7th-grade campers preferred the mountains" is incorrect.

2. Absolute Number of 8th Graders who preferred Seacoast:
   • Total 8th Grade Students = 200.
   • Number of 8th Graders who preferred Seacoast = 90.
   • Relative Frequency = (90/200) * 100 = 45%.

So, the statement "90% of 8th-grade campers preferred the seacoast" is incorrect.

3. Relative Frequency of 8th Graders who preferred Mountains:
   • Number of 8th Graders who preferred Mountains = 110.
   • Total number of students who preferred Mountains = 150.
   • Relative Frequency = (110/150) * 100 ≈ 73.33%, which when rounded to the nearest tenth is 73.3%.

Thus, the statement "70% of the people who preferred mountains were 8th graders" is approximately correct but slightly understated.

4. Relative Frequency of 7th Graders who preferred Seacoast:
   • Number of 7th Graders who preferred Seacoast = 60.
   • Total number who preferred Seacoast = 150.
   • Relative Frequency = (60/150) * 100 = 40%.

Thus, the statement "40% of the people who preferred the seacoast were 7th graders" is correct.

Conclusion

The correct relative frequency from the options provided is:

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