Question
50 students are randomly selected and 4 own cats. If there are 800 students, use a proportion to estimate how many of them own cats?
Answers
GPT-4o mini
To estimate how many students own cats among the total of 800 students using the proportion of the sample, you can set up a proportion based on the data from the 50 students surveyed.
In the sample of 50 students, 4 own cats. To find the proportion of students who own cats in the sample, you can calculate:
\[
\text{Proportion of students owning cats} = \frac{\text{Number of students owning cats}}{\text{Total number of students in sample}} = \frac{4}{50}
\]
Now, to find out how many students in the total population of 800 students would own cats, you can multiply this proportion by 800:
\[
\text{Estimated number of students owning cats} = \left(\frac{4}{50}\right) \times 800
\]
Calculating this:
\[
\text{Estimated number of students owning cats} = \frac{4 \times 800}{50} = \frac{3200}{50} = 64
\]
Thus, we estimate that approximately **64 students** own cats out of the total 800 students.
In the sample of 50 students, 4 own cats. To find the proportion of students who own cats in the sample, you can calculate:
\[
\text{Proportion of students owning cats} = \frac{\text{Number of students owning cats}}{\text{Total number of students in sample}} = \frac{4}{50}
\]
Now, to find out how many students in the total population of 800 students would own cats, you can multiply this proportion by 800:
\[
\text{Estimated number of students owning cats} = \left(\frac{4}{50}\right) \times 800
\]
Calculating this:
\[
\text{Estimated number of students owning cats} = \frac{4 \times 800}{50} = \frac{3200}{50} = 64
\]
Thus, we estimate that approximately **64 students** own cats out of the total 800 students.