In a school with 2,000 students, a random sample of 120 students were asked which fruit is their favorite. Their responses are shown in the table below.

Survey Responses
Favorite Fruit
Number of Students
Banana
23
Apple
18
Orange
34
Peach
27
Pear
18

Using proportional reasoning, about how many students out of the 2,000 would you expect to select an orange as their favorite fruit?
about 34 students
about 58 students
about 283 students
about 567 students

1 answer

To find out how many students out of 2,000 would be expected to select an orange as their favorite fruit, we can use proportional reasoning based on the sample data.

From the survey, the number of students who selected orange is 34, and the total number of students surveyed is 120.

First, we calculate the proportion of students who selected orange in the sample:

\[ \text{Proportion of orange lovers} = \frac{34}{120} \]

Next, we can find this proportion and then apply it to the entire student population of 2,000:

\[ \text{Proportion of orange lovers} = \frac{34}{120} \approx 0.2833 \]

Now, we use this proportion to estimate the number of students in the school who would select orange as their favorite fruit:

\[ \text{Expected number of orange lovers} = 0.2833 \times 2000 \]

Calculating this gives:

\[ 0.2833 \times 2000 \approx 566.6 \]

Rounding this value, we find that approximately 567 students out of the total 2,000 are expected to select an orange as their favorite fruit.

Therefore, the answer is: about 567 students.