Question

example
garrett is running for class president. he wants to know if he is likely to win, so his friend kosumi surveys a random sample of 10 students in his school. of the 10 students, 7 plan to vote for garrett. suppose all 233 students in the school vote in the election for class president. about how many students should garrett expect to vote for him?
since \\(\frac{7}{10}\\) of students in the sample plan to vote for garrett, he should expect about \\(\frac{7}{10}\\) of the population to vote for him.
\\(\frac{7}{10}(233) = 163\frac{1}{10}\\)
garrett should expect about 163 students to vote for him.
1 kosumi conducts another survey of students in the school in the example. this time, he surveys a random sample of 30 students.
a. in kosumi’s sample, 24 students plan to vote for garrett. based on this sample, about how many students in the school should garrett expect to vote for him?
show your work.

Explanation:

Step1: Find the fraction of students in the sample who plan to vote for Garrett.

In the sample of 30 students, 24 plan to vote for Garrett. So the fraction is $\frac{24}{30}$. We can simplify this fraction: $\frac{24\div6}{30\div6}=\frac{4}{5}$.

Step2: Multiply this fraction by the total number of students in the school.

The total number of students in the school is 233. So we calculate $\frac{4}{5}\times233$.
First, $233\div5 = 46.6$, then $46.6\times4 = 186.4$. Since we are dealing with the number of students, we can also calculate it as $\frac{4\times233}{5}=\frac{932}{5}=186.4$. We can round this to a whole number, but since we are approximating, we can say about 186 or 186.4. But let's do the exact multiplication: $24\div30 = 0.8$, then $0.8\times233 = 186.4$. So Garrett should expect about 186 (or 186.4) students to vote for him.

Answer:

To determine how many students Garrett should expect to vote for him, follow these steps:

Step 1: Find the proportion of students in the sample who support Garrett.

In the sample of 30 students, 24 plan to vote for Garrett. The proportion is:
$$\frac{24}{30} = \frac{4}{5} = 0.8$$

Step 2: Apply this proportion to the total school population.

The total number of students in the school is 233. Multiply the proportion by 233:
$$0.8 \times 233 = 186.4$$

Since we cannot have a fraction of a student, we can approximate. Garrett should expect about $\boldsymbol{186}$ (or $186.4$) students to vote for him. (If rounding to the nearest whole number, the answer is 186.)