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The table shows the results of a survey to find what type of breakfast students preferred. Each student could only select one choice.

The tables show that 10 students perfer eggs 2 perfer cearal and 8 perfer toast

Use the table to determine whether the following statements are true or false.

(3 points)
True False
The sample space is 20.

The experimental probability of students preferring cereal is 110

The relative frequency for students preferring toast is 0.8

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1 answer

To analyze the statements based on the survey results, we need to determine a few key pieces of information:

  1. The total number of students surveyed.
  2. The experimental probability of students preferring cereal.
  3. The relative frequency of students preferring toast.

From the information given:

  • Students preferring eggs: 10
  • Students preferring cereal: 2
  • Students preferring toast: 8

Total Number of Students

To find the total number of students surveyed, we sum the preferences:

Total = Students preferring eggs + Students preferring cereal + Students preferring toast
Total = 10 + 2 + 8 = 20

Statement Analysis

  1. The sample space is 20.
    This statement is True.

  2. The experimental probability of students preferring cereal is 110.
    The experimental probability is calculated by dividing the number of students who preferred cereal by the total number of students surveyed:
    Probability of cereal = Students preferring cereal / Total students = 2 / 20 = 0.1.
    Since 110 does not equate to the probability we calculated, this statement is False.

  3. The relative frequency for students preferring toast is 0.8.
    The relative frequency for toast is calculated by dividing the number of students who preferred toast by the total number of students surveyed:
    Relative frequency for toast = Students preferring toast / Total students = 8 / 20 = 0.4.
    Since 0.4 is not equal to 0.8, this statement is False.

Summary

  • The sample space is 20: True
  • The experimental probability of students preferring cereal is 110: False
  • The relative frequency for students preferring toast is 0.8: False