Question

question 2 of 10

northlake high school has two lunch periods. students can eat their lunch in the cafeteria or on an outside patio. about 31% of students who have first lunch eat outside. compare this with the percentage of second-lunch students who eat outside.

select the true statement.

a. a smaller percentage of second-lunch students (24%) eat outside.
b. a greater percentage of second-lunch students (45%) eat outside.
c. a smaller percentage of second-lunch students (21%) eat outside.
d. a greater percentage of second-lunch students (47%) eat outside.

Explanation:

Identify the given values

We are given a two-way relative frequency table:

• Joint relative frequency of second-lunch students who eat outside: \(0.21\)
• Marginal relative frequency of second-lunch students: \(0.45\)
• First-lunch students eating outside: \(31\%\)

Formulate the target calculation

We need to find the conditional percentage of second-lunch students who eat outside:

$$ P(\text{Eat outside} \mid \text{Second lunch}) = \frac{P(\text{Second lunch and Eat outside})}{P(\text{Second lunch})} $$

Calculate the conditional percentage

Using the values from the table:

$$ P(\text{Eat outside} \mid \text{Second lunch}) = \frac{0.21}{0.45} \approx 0.4667 = 46.67\% \approx 47\% $$

Compare the percentages

We compare the two percentages:

• First-lunch students eating outside: \(31\%\)
• Second-lunch students eating outside: \(47\%\)
• Since \(47\% > 31\%\), a greater percentage of second-lunch students eat outside.

Match with the options

We evaluate the given choices:

• Option D states: "A greater percentage of second-lunch students (47%) eat outside." This matches our calculation.

Answer:

• A. A smaller percentage of second-lunch students (24%) eat outside.
• B. A greater percentage of second-lunch students (45%) eat outside.
• C. A smaller percentage of second-lunch students (21%) eat outside.
• D. A greater percentage of second-lunch students (47%) eat outside. (Correct answer)