High School

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!

Select the correct answer.

[tex]
\[
\begin{array}{|c|c|c|c|c|}
\hline
\text{Weight/Calories per Day} & \text{1000 to 1500 cal.} & \text{1500 to 2000 cal.} & \text{2000 to 2500 cal.} & \text{Total} \\
\hline
\text{120 lb.} & 90 & 80 & 10 & 180 \\
\hline
\text{145 lb.} & 35 & 143 & 25 & 203 \\
\hline
\text{165 lb.} & 15 & 27 & 75 & 117 \\
\hline
\text{Total} & 140 & 250 & 110 & 500 \\
\hline
\end{array}
\]
[/tex]

Based on the data in the two-way table, which statement is true?

A. [tex] P(\text{consumes 1000-1500 calories} \mid \text{weight is 165}) = P(\text{consumes 1000-1500 calories}) [/tex]

B. [tex] P(\text{weight is 120 lb.} \mid \text{consumes 2000-2500 calories}) \neq P(\text{weight is 120 lb.}) [/tex]

C. [tex] P(\text{weight is 165 lb.} \mid \text{consumes 1000-2000 calories}) = P(\text{weight is 165 lb.}) [/tex]

D. [tex] P(\text{weight is 145 lb.} \mid \text{consumes 1000-2000 calories}) = P(\text{consumes 1000-2000 calories}) [/tex]

Answer :

Let's carefully analyze each statement from the data in the two-way table and determine which one is true:

### Total Probabilities:
First, we find the totals needed:
- Total weight = 500: The sum of all individuals (180 + 203 + 117).
- Total calories of each range:
- 1000-1500 cal: 140.
- 1500-2000 cal: 250.
- 2000-2500 cal: 110.

- Total by weight:
- 120 lb: 180.
- 145 lb: 203.
- 165 lb: 117.

### Checking Each Statement:

A. [tex]\( P(\text{consumes 1000-1500 calories} \mid \text{weight is 165}) = P(\text{consumes 1000-1500 calories}) \)[/tex]

- Probability of consuming 1000-1500 calories given weight is 165:
[tex]\(\frac{15}{117}\)[/tex].

- Probability of consuming 1000-1500 calories:
[tex]\(\frac{140}{500}\)[/tex].

Since [tex]\(\frac{15}{117} \neq \frac{140}{500}\)[/tex], this statement is false.

B. [tex]\( P(\text{weight is 120 lb} \mid \text{consumes 2000-2500 calories}) \neq P(\text{weight is 120 lb}) \)[/tex]

- Probability of weight being 120 lb given consumes 2000-2500 calories:
[tex]\(\frac{10}{110}\)[/tex].

- Probability of weight being 120 lb:
[tex]\(\frac{180}{500}\)[/tex].

Since [tex]\(\frac{10}{110} \neq \frac{180}{500}\)[/tex], this statement is true.

C. [tex]\( P(\text{weight is 165 lb} \mid \text{consumes 1000-2000 calories}) = P(\text{weight is 165 lb}) \)[/tex]

- Probability of weight being 165 lb given consumes 1000-2000 calories:
[tex]\(\frac{15 + 27}{140 + 250} = \frac{42}{390}\)[/tex].

- Probability of weight being 165 lb:
[tex]\(\frac{117}{500}\)[/tex].

Since [tex]\(\frac{42}{390} \neq \frac{117}{500}\)[/tex], this statement is false.

D. [tex]\( P(\text{weight is 145 lb} \mid \text{consumes 1000-2000 calories}) = P(\text{consumes 1000-2000 calories}) \)[/tex]

- Probability of weight being 145 lb given consumes 1000-2000 calories:
[tex]\(\frac{35 + 143}{140 + 250} = \frac{178}{390}\)[/tex].

- Probability of consuming 1000-2000 calories:
[tex]\(\frac{390}{500}\)[/tex].

Since [tex]\(\frac{178}{390} \neq \frac{390}{500}\)[/tex], this statement is false.

### Conclusion:
Statement B is the only true statement among the four.

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!

Rewritten by : Barada