Question

Nate wants to know how many of the students in his school have a younger sibling. He surveys a random sample of 25 students at his school, and 14 of those students have a younger sibling. If the whole school has 800 students, how many would be expected to have a younger sibling?
students

Answer 1

To estimate how many students in the entire school have a younger sibling, we can first find the proportion of students in Nate's sample who have a younger sibling.

In Nate's survey:
- Total students surveyed = 25
- Students with a younger sibling = 14

The proportion of students with a younger sibling in the sample is:

\[
\text{Proportion} = \frac{14}{25}
\]

Now we'll use this proportion to estimate how many students in the entire school (800 students) are expected to have a younger sibling. We will multiply the proportion by the total number of students in the school.

First, calculate the proportion:

\[
\text{Proportion} = \frac{14}{25} = 0.56
\]

Now we multiply this proportion by the total number of students in the school:

\[
\text{Expected number of students with a younger sibling} = 0.56 \times 800
\]

Calculating that:

\[
0.56 \times 800 = 448
\]

Thus, we would expect **448 students** in the entire school to have a younger sibling.