Select the correct answer.

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

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

A. [tex]\( P(\text{consumes } 1,000-1,500 \text{ calories} \mid \text{weight is } 165 \text{ lb.}) = P(\text{consumes } 1,000-1,500 \text{ calories}) \)[/tex]

B. [tex]\( P(\text{weight is 120 lb.} \mid \text{consumes } 2,000-2,500 \text{ calories}) = P(\text{weight is 120 lb.}) \)[/tex]

C. [tex]\( P(\text{weight is 165 lb.} \mid \text{consumes } 1,000-2,000 \text{ calories}) = P(\text{weight is 165 lb.}) \)[/tex]

D. [tex]\( P(\text{weight is 145 lb.} \mid \text{consumes } 1,000-2,000 \text{ calories}) = P(\text{consumes } 1,000-2,000 \text{ calories}) \)[/tex]

To determine which statement is true based on the given data, we examine the probabilities related to the choices:

A. P(consumes 1000-1500 calories | weight is 165 lb) = P(consumes 1000-1500 calories)

- Calculate P(consumes 1000-1500 calories | weight is 165 lb):

- Out of the 117 people who weigh 165 lb, 15 consume 1000-1500 calories.
- Probability = 15 / 117

- Calculate P(consumes 1000-1500 calories):

- Out of the total 500 people, 140 consume 1000-1500 calories.
- Probability = 140 / 500

The probabilities are not equal, so this statement is false.

B. P(weight is 120 lb | consumes 2000-2500 calories) vs. P(weight is 120 lb)

These probabilities are different, but since the statement doesn't claim they are equal, it is not something we assess for equality in this problem.

C. P(weight is 165 lb | consumes 1000-2000 calories) = P(weight is 165 lb)

- Calculate P(weight is 165 lb | consumes 1000-2000 calories):

- 15 people weighing 165 lb consume 1000-1500 calories, and 27 consume 1500-2000 calories.
- Total consuming 1000-2000 calories = 140 + 250 = 390
- Probability = (15 + 27) / 390

- Calculate P(weight is 165 lb):

- Out of the total 500 people, 117 weigh 165 lb.
- Probability = 117 / 500

The probabilities are not equal, so this statement is false.

D. P(weight is 145 lb | consumes 1000-2000 calories) = P(consumes 1000-2000 calories)

- Calculate P(weight is 145 lb | consumes 1000-2000 calories):

- 35 people weighing 145 lb consume 1000-1500 calories, and 143 consume 1500-2000 calories.
- Total consuming 1000-2000 calories = 140 + 250 = 390
- Probability = (35 + 143) / 390

- Calculate P(consumes 1000-2000 calories):

- Total consuming 1000-2000 calories = 140 + 250 = 390
- Probability = 390 / 500

The probabilities are not equal, so this statement is false.

Based on the analysis, all statements are false. The final choice would be either choosing none if that's an option or acknowledging none of them are true.