To solve this problem, we need to estimate how many people out of the total attendance of 5,000 would prefer mustard on their hot dogs based on the provided sample data.
Here's a step-by-step approach to solving this problem:
1. Identify the total number of people in the sample: From the data provided, we know that 150 people were asked about their hot dog preference.
2. Identify the number of people in the sample who prefer mustard: According to the table, 27 out of 150 people prefer mustard on their hot dogs.
3. Calculate the proportion of people in the sample who prefer mustard:
[tex]\[
\text{Proportion of mustard preferers} = \frac{\text{Number who prefer mustard}}{\text{Total sample size}} = \frac{27}{150}
\][/tex]
4. Simplify the proportion:
[tex]\[
\frac{27}{150} = 0.18
\][/tex]
This means that 18% of the sample prefers mustard on their hot dogs.
5. Estimate the number of people out of the total attendance who would prefer mustard: We apply the proportion we found to the total attendance of 5,000 people.
[tex]\[
\text{Estimated number who prefer mustard} = \text{Proportion of mustard preferers} \times \text{Total attendance} = 0.18 \times 5000
\][/tex]
6. Perform the multiplication:
[tex]\[
0.18 \times 5000 = 900
\][/tex]
So, based on the data in this sample, it is estimated that 900 people out of the 5,000 in attendance would prefer mustard on their hot dogs.
Thus, the correct answer is:
[tex]\[
\boxed{900}
\][/tex]
