To estimate how many students in the entire school prefer orange sherbet based on Pablo's survey, we first need to determine the proportion of students who prefer orange sherbet in the sample.
From the survey results, 10 out of the 130 surveyed students prefer orange sherbet. We can calculate the proportion as follows:
\[ \text{Proportion for Orange Sherbet} = \frac{\text{number of students who prefer Orange Sherbet}}{\text{total number of surveyed students}} = \frac{10}{130} \]
Now, let's simplify that fraction:
\[ \frac{10}{130} = \frac{1}{13} \]
Now, we will use this proportion to estimate how many students in the entire school of 528 students prefer orange sherbet:
\[ \text{Estimated number of students preferring Orange Sherbet} = \text{Proportion} \times \text{Total number of students} \]
\[ = \frac{1}{13} \times 528 \]
Calculating this gives:
\[ = 40.6154 \text{ (approximately 41)} \]
So the closest estimate for the number of students who prefer orange sherbet is 41.