We appreciate your visit to Select the correct answer tex begin array c c c c c hline text Weight Calories per Day text 1000 to 1500 cal text 1500. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Let's analyze each statement based on the data provided.
First, let's explain what these probability expressions represent:
- Conditional Probability: This is the probability of an event occurring given that another event has occurred. It is represented as [tex]\( P(A \mid B) \)[/tex], meaning the probability of [tex]\( A \)[/tex] given [tex]\( B \)[/tex].
Now, let's break down each statement:
Statement A:
- [tex]\( P(\text{consumes } 1,000-1,500 \text{ calories} \mid \text{weight is 165}) \)[/tex]
- This is the probability of someone consuming 1,000-1,500 calories given they weigh 165 lb.
- From the table: 15 people weigh 165 lb. and consume 1,000-1,500 calories, and a total of 117 people weigh 165 lb.
- Probability: [tex]\( \frac{15}{117} \)[/tex].
- [tex]\( P(\text{consumes } 1,000-1,500 \text{ calories}) \)[/tex]
- This is the probability of someone consuming 1,000-1,500 calories overall.
- From the table: 140 people consume 1,000-1,500 calories out of a total of 500 people.
- Probability: [tex]\( \frac{140}{500} \)[/tex].
Since these two probabilities do not match, statement A is false.
Statement B:
- [tex]\( P(\text{weight is } 120 \text{ lb} \mid \text{consumes } 2,000-2,500 \text{ calories}) \)[/tex]
- This is the probability of someone being 120 lb given they consume 2,000-2,500 calories.
- From the table: 10 people consume 2,000-2,500 calories with a weight of 120 lb. The total number of people consuming 2,000-2,500 calories is 110.
- Probability: [tex]\( \frac{10}{110} \)[/tex].
- [tex]\( P(\text{weight is } 120 \text{ lb}) \)[/tex]
- This is the probability of someone weighing 120 lb regardless of calorie consumption.
- From the table: 180 people weigh 120 lb out of a total of 500 people.
- Probability: [tex]\( \frac{180}{500} \)[/tex].
Since these probabilities are not equal, statement B is true.
Statement C:
- [tex]\( P(\text{weight is 165 lb consumes } 1,000-2,000 \text{ calories}) \)[/tex]
- Here, we combine the probabilities for calories 1,000-1,500 and 1,500-2,000.
- From the table: 15 (for 1,000-1,500) + 27 (for 1,500-2,000) = 42 people fit both conditions, with a total weight category of 165 lb.
- Probability (given we're considering only those who weigh 165 lb): [tex]\( \frac{42}{117} \)[/tex].
- [tex]\( P(\text{weight is 165 lb}) \)[/tex]
- As calculated before, the probability is [tex]\( \frac{117}{500} \)[/tex].
These probabilities are not equal, so statement C is false.
Statement D:
- [tex]\( P(\text{weight is 145 lb} \mid \text{consumes } 1,000-2,000 \text{ calories}) \)[/tex]
- From the table for consuming 1,000-2,000 calories: 35 (for 1,000-1,500) + 143 (for 1,500-2,000) = 178 people with weight 145 lb.
- Total consuming these calories is 140 + 250 = 390 people.
- Probability: [tex]\( \frac{178}{390} \)[/tex].
- [tex]\( P(\text{consumes } 1,000-2,000 \text{ calories}) \)[/tex]
- Calculated total consuming 1,000-2,000 calories out of the total 500 people.
- Probability: [tex]\( \frac{390}{500} \)[/tex].
These probabilities are not equal, so statement D is false.
The correct statement after analyzing the data is Statement B.
First, let's explain what these probability expressions represent:
- Conditional Probability: This is the probability of an event occurring given that another event has occurred. It is represented as [tex]\( P(A \mid B) \)[/tex], meaning the probability of [tex]\( A \)[/tex] given [tex]\( B \)[/tex].
Now, let's break down each statement:
Statement A:
- [tex]\( P(\text{consumes } 1,000-1,500 \text{ calories} \mid \text{weight is 165}) \)[/tex]
- This is the probability of someone consuming 1,000-1,500 calories given they weigh 165 lb.
- From the table: 15 people weigh 165 lb. and consume 1,000-1,500 calories, and a total of 117 people weigh 165 lb.
- Probability: [tex]\( \frac{15}{117} \)[/tex].
- [tex]\( P(\text{consumes } 1,000-1,500 \text{ calories}) \)[/tex]
- This is the probability of someone consuming 1,000-1,500 calories overall.
- From the table: 140 people consume 1,000-1,500 calories out of a total of 500 people.
- Probability: [tex]\( \frac{140}{500} \)[/tex].
Since these two probabilities do not match, statement A is false.
Statement B:
- [tex]\( P(\text{weight is } 120 \text{ lb} \mid \text{consumes } 2,000-2,500 \text{ calories}) \)[/tex]
- This is the probability of someone being 120 lb given they consume 2,000-2,500 calories.
- From the table: 10 people consume 2,000-2,500 calories with a weight of 120 lb. The total number of people consuming 2,000-2,500 calories is 110.
- Probability: [tex]\( \frac{10}{110} \)[/tex].
- [tex]\( P(\text{weight is } 120 \text{ lb}) \)[/tex]
- This is the probability of someone weighing 120 lb regardless of calorie consumption.
- From the table: 180 people weigh 120 lb out of a total of 500 people.
- Probability: [tex]\( \frac{180}{500} \)[/tex].
Since these probabilities are not equal, statement B is true.
Statement C:
- [tex]\( P(\text{weight is 165 lb consumes } 1,000-2,000 \text{ calories}) \)[/tex]
- Here, we combine the probabilities for calories 1,000-1,500 and 1,500-2,000.
- From the table: 15 (for 1,000-1,500) + 27 (for 1,500-2,000) = 42 people fit both conditions, with a total weight category of 165 lb.
- Probability (given we're considering only those who weigh 165 lb): [tex]\( \frac{42}{117} \)[/tex].
- [tex]\( P(\text{weight is 165 lb}) \)[/tex]
- As calculated before, the probability is [tex]\( \frac{117}{500} \)[/tex].
These probabilities are not equal, so statement C is false.
Statement D:
- [tex]\( P(\text{weight is 145 lb} \mid \text{consumes } 1,000-2,000 \text{ calories}) \)[/tex]
- From the table for consuming 1,000-2,000 calories: 35 (for 1,000-1,500) + 143 (for 1,500-2,000) = 178 people with weight 145 lb.
- Total consuming these calories is 140 + 250 = 390 people.
- Probability: [tex]\( \frac{178}{390} \)[/tex].
- [tex]\( P(\text{consumes } 1,000-2,000 \text{ calories}) \)[/tex]
- Calculated total consuming 1,000-2,000 calories out of the total 500 people.
- Probability: [tex]\( \frac{390}{500} \)[/tex].
These probabilities are not equal, so statement D is false.
The correct statement after analyzing the data is Statement B.
Thanks for taking the time to read Select the correct answer tex begin array c c c c c hline text Weight Calories per Day text 1000 to 1500 cal text 1500. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
