High School

Interpreting Two-Way Frequency Tables: Mastery Test

Select the correct answer.

[tex]\[

\begin{tabular}{|c|c|c|c|c|}

\hline

Weight/Calories per Day & $1000$ to $1500$ cal. & $1500$ to $2000$ cal. & $2000$ to $2500$ cal. & Total \\

\hline

$120$ lb & 90 & 80 & 10 & 180 \\

\hline

$145$ lb & 35 & 143 & 25 & 203 \\

\hline

$165$ lb & 15 & 27 & 75 & 117 \\

\hline

Total & 140 & 250 & 110 & 500 \\

\hline

\end{tabular}

\][/tex]

Based on the data in the two-way table, what is the probability that a person consumes 1,500 to 2,000 calories?

A. 0.22
B. 0.28
C. 0.35
D. 0.50

Answer :

To determine the probability that a person consumes between 1,500 and 2,000 calories per day, we can follow these steps:

1. First, let's identify the total number of respondents in the survey. According to the table, the total number of people surveyed is 500.

2. Next, we need to find the total number of people who consume between 1,500 and 2,000 calories per day. By looking at the table, we can see that in the column titled "1,500 to 2,000 cal," the total number is 250.

3. Now that we know 250 people consume between 1,500 and 2,000 calories, we need to calculate the probability by dividing the number of people in this calorie range by the total number of people surveyed.

The probability calculation is as follows:

[tex]\[
\text{Probability} = \frac{\text{Number of people consuming 1,500 to 2,000 cal}}{\text{Total number of people}} = \frac{250}{500} = 0.5
\][/tex]

Therefore, the probability that a person consumes 1,500 to 2,000 calories is 0.5.

So, the correct answer is D. 0.50.