In a survey, people are classified based on whether they can see the sunrise, the sunset, both, or neither. Which of the following best describes the joint relative frequency for the people who can only see the sunset?

• A. The proportion of all people surveyed who cannot see the sunset
• B. The proportion of all people surveyed who can see the sunset but not the sunrise
• C. The proportion of all people surveyed who can see both the sunrise and the sunset
• D. The proportion of all people surveyed who can see either the sunrise or the sunset

Answer: (B)

Verified step by step guidance

1. Understand that joint relative frequency refers to the proportion of the total population that falls into a specific combined category—in this case, people who can only see the sunset.
2. Identify the group of interest: those who can see the sunset but not the sunrise. This is a joint event involving two conditions: 'can see sunset' AND 'cannot see sunrise'.
3. Express the joint relative frequency mathematically as the number of people who can see the sunset but not the sunrise divided by the total number of people surveyed. This can be written as \(\frac{\text{Number who see sunset only}}{\text{Total number surveyed}}\).
4. Recognize that this joint relative frequency is different from the proportion who cannot see the sunset, who can see both sunrise and sunset, or who can see either sunrise or sunset, because those describe different subsets or unions of the data.
5. Conclude that the best description of the joint relative frequency for people who can only see the sunset is the proportion of all people surveyed who can see the sunset but not the sunrise.