Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Get quick and reliable solutions to your questions from a community of experienced professionals on our platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
To determine which statement is true, we need to compare the probabilities given in the statements. Let's start by calculating the relevant probabilities.
### Given Data:
- Total number of people = 500
- Breakdown by weight:
- 120 lbs: 180 people
- 145 lbs: 203 people
- 165 lbs: 117 people
- Breakdown by calories:
- 1000-1500 calories: 140 people
- 1500-2000 calories: 250 people
- 2000-2500 calories: 110 people
### Statement A: [tex]\( P(\text{consumes 1000-1500 calories} | \text{weight is 165}) = P(\text{consumes 1000-1500 calories}) \)[/tex]
- [tex]\( P(\text{weight is 165}) = \frac{117}{500} \)[/tex]
- [tex]\( P(\text{consumes 1000-1500 calories} | \text{weight is 165}) = \frac{15}{117} \)[/tex]
- [tex]\( P(\text{consumes 1000-1500 calories}) = \frac{140}{500} \)[/tex]
Comparing these values, they are not equal:
[tex]\[ \frac{15}{117} \neq \frac{140}{500} \][/tex]
### Statement B: [tex]\( P(\text{weight is 120 lbs} \cap \text{consumes 2000-2500 calories}) \neq P(\text{weight is 120 lbs}) \)[/tex]
- [tex]\( P(\text{weight is 120 lbs}) = \frac{180}{500} \)[/tex]
- [tex]\( P(\text{weight is 120 lbs} \cap \text{consumes 2000-2500 calories}) = \frac{10}{500} \)[/tex]
Comparing these values, they are not equal:
[tex]\[ \frac{10}{500} \neq \frac{180}{500} \][/tex]
### Statement C: [tex]\( P(\text{weight is 165 lbs} \cap \text{consumes 1000-2000 calories}) = P(\text{weight is 165 lbs}) \)[/tex]
- [tex]\( P(\text{weight is 165 lbs}) = \frac{117}{500} \)[/tex]
- [tex]\( P(\text{weight is 165 lbs} \cap \text{consumes 1000-2000 calories}) = \frac{15 + 27}{500} = \frac{42}{500} \)[/tex]
Comparing these values, they are not equal:
[tex]\[ \frac{42}{500} \neq \frac{117}{500} \][/tex]
### Statement D: [tex]\( P(\text{weight is 145 lbs and consumes 1000-2000 calories}) = P(\text{consumes 1000-2000 calories}) \)[/tex]
- [tex]\( P(\text{weight is 145 lbs and consumes 1000-2000 calories}) = \frac{35 + 143}{500} = \frac{178}{500} \)[/tex]
- [tex]\( P(\text{consumes 1000-2000 calories}) = \frac{140 + 250}{500} = \frac{390}{500} \)[/tex]
Comparing these values, they are not equal:
[tex]\[ \frac{178}{500} \neq \frac{390}{500} \][/tex]
Based on these calculations, we find that only Statement B is true. Therefore, the correct answer is:
### Statement B. [tex]\( P(\text{weight is 120 lbs} \cap \text{consumes 2000-2500 calories}) \neq P(\text{weight is 120 lbs}) \)[/tex]
### Given Data:
- Total number of people = 500
- Breakdown by weight:
- 120 lbs: 180 people
- 145 lbs: 203 people
- 165 lbs: 117 people
- Breakdown by calories:
- 1000-1500 calories: 140 people
- 1500-2000 calories: 250 people
- 2000-2500 calories: 110 people
### Statement A: [tex]\( P(\text{consumes 1000-1500 calories} | \text{weight is 165}) = P(\text{consumes 1000-1500 calories}) \)[/tex]
- [tex]\( P(\text{weight is 165}) = \frac{117}{500} \)[/tex]
- [tex]\( P(\text{consumes 1000-1500 calories} | \text{weight is 165}) = \frac{15}{117} \)[/tex]
- [tex]\( P(\text{consumes 1000-1500 calories}) = \frac{140}{500} \)[/tex]
Comparing these values, they are not equal:
[tex]\[ \frac{15}{117} \neq \frac{140}{500} \][/tex]
### Statement B: [tex]\( P(\text{weight is 120 lbs} \cap \text{consumes 2000-2500 calories}) \neq P(\text{weight is 120 lbs}) \)[/tex]
- [tex]\( P(\text{weight is 120 lbs}) = \frac{180}{500} \)[/tex]
- [tex]\( P(\text{weight is 120 lbs} \cap \text{consumes 2000-2500 calories}) = \frac{10}{500} \)[/tex]
Comparing these values, they are not equal:
[tex]\[ \frac{10}{500} \neq \frac{180}{500} \][/tex]
### Statement C: [tex]\( P(\text{weight is 165 lbs} \cap \text{consumes 1000-2000 calories}) = P(\text{weight is 165 lbs}) \)[/tex]
- [tex]\( P(\text{weight is 165 lbs}) = \frac{117}{500} \)[/tex]
- [tex]\( P(\text{weight is 165 lbs} \cap \text{consumes 1000-2000 calories}) = \frac{15 + 27}{500} = \frac{42}{500} \)[/tex]
Comparing these values, they are not equal:
[tex]\[ \frac{42}{500} \neq \frac{117}{500} \][/tex]
### Statement D: [tex]\( P(\text{weight is 145 lbs and consumes 1000-2000 calories}) = P(\text{consumes 1000-2000 calories}) \)[/tex]
- [tex]\( P(\text{weight is 145 lbs and consumes 1000-2000 calories}) = \frac{35 + 143}{500} = \frac{178}{500} \)[/tex]
- [tex]\( P(\text{consumes 1000-2000 calories}) = \frac{140 + 250}{500} = \frac{390}{500} \)[/tex]
Comparing these values, they are not equal:
[tex]\[ \frac{178}{500} \neq \frac{390}{500} \][/tex]
Based on these calculations, we find that only Statement B is true. Therefore, the correct answer is:
### Statement B. [tex]\( P(\text{weight is 120 lbs} \cap \text{consumes 2000-2500 calories}) \neq P(\text{weight is 120 lbs}) \)[/tex]
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.
