To determine how many students from the entire college population might prefer cookies, we can use the data from the sample of 225 students. Here’s the step-by-step process:
1. Identify the Total Population and Sample Size:
The total number of students in the college is 4,000.
The number of students sampled is 225.
2. Identify the Number of Students in the Sample Who Prefer Cookies:
According to the table, 27 out of 225 sampled students prefer cookies.
3. Calculate the Proportion of Students in the Sample Who Prefer Cookies:
The proportion (or ratio) can be calculated by dividing the number of students who prefer cookies by the total number of students sampled:
[tex]\[
\text{Proportion} = \frac{\text{Number of students who prefer cookies}}{\text{Total number of students sampled}} = \frac{27}{225}
\][/tex]
This proportion simplifies to:
[tex]\[
\text{Proportion} = 0.12
\][/tex]
4. Use the Proportion to Predict the Number of Students in the Total Population Who Prefer Cookies:
To estimate the number of students in the entire college who would prefer cookies, we multiply this proportion by the total number of students:
[tex]\[
\text{Predicted number of students who prefer cookies} = \text{Proportion} \times \text{Total number of students} = 0.12 \times 4,000
\][/tex]
This calculation results in:
[tex]\[
0.12 \times 4,000 = 480
\][/tex]
Hence, based on the sampling data, the best prediction about the number of cookies the college will need is that approximately 480 students will prefer cookies.
Correct Answer:
The college will have about 480 students who prefer cookies.
