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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, what is the probability that a person weighs 120 pounds, given that he or she consumes 2,000 to 2,500 calories per day?

A. 0.09
B. 0.12
C. 0.22
D. 0.35

Answer :

To find the probability that a person weighs 120 pounds, given that he or she consumes 2,000 to 2,500 calories per day, we need to focus on the relevant data from the table.

Here's a step-by-step method to solve the problem:

1. Identify the desired condition: We are given that the person consumes 2,000 to 2,500 calories per day.

2. Find the total number of people who consume 2,000 to 2,500 calories per day: According to the table, a total of 110 people consume between 2,000 to 2,500 calories.

3. Determine the number of people who weigh 120 pounds within this group: Out of those who consume 2,000 to 2,500 calories, 10 people weigh 120 pounds.

4. Calculate the probability: Probability is defined as the number of favorable outcomes divided by the total number of possible outcomes. In this case, the probability is:

[tex]\[
\text{Probability} = \frac{\text{Number of 120-pound people consuming 2,000 to 2,500 calories}}{\text{Total number of people consuming 2,000 to 2,500 calories}}
\][/tex]

Plugging in the values we have:

[tex]\[
\text{Probability} = \frac{10}{110} \approx 0.0909
\][/tex]

So, the probability that a person weighs 120 pounds given that they consume 2,000 to 2,500 calories per day is approximately 0.09 or 9%. Hence, the correct answer is:

A. 0.09

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