Question

Ann randomly surveyed 36 students to see if there was interest in sharing a seventh-grade science club. He found that 4 students said they would be interested. If 180 students are in the seventh grade, how many can be expected to join?

Answer 1

To find the expected number of students who would be interested in joining the science club from the total population of seventh-grade students, we first determine the proportion of students in Ann's sample who expressed interest in the club.

Ann surveyed 36 students, and 4 of them indicated interest. The proportion of interested students can be calculated as:

\[
\text{Proportion of interested students} = \frac{\text{Number of interested students}}{\text{Total surveyed students}} = \frac{4}{36}
\]

Next, we simplify this fraction:

\[
\frac{4}{36} = \frac{1}{9}
\]

This means that approximately \(\frac{1}{9}\) of the surveyed students are interested in the science club. To find how many seventh-grade students out of the total 180 can be expected to join, we multiply the total number of seventh-grade students by this proportion:

\[
\text{Expected number of interested students} = \text{Total students} \times \text{Proportion of interested students}
\]

Substituting in the values:

\[
\text{Expected number of interested students} = 180 \times \frac{1}{9}
\]

Now, performing the multiplication:

\[
180 \times \frac{1}{9} = 20
\]

Thus, the expected number of students who will join the seventh-grade science club is

\[
\boxed{20}
\]