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?

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.