To estimate how many students in the whole school prefer orange sherbet based on Pablo's sample data, we can set up a proportion based on the number of students surveyed and the total number of students at the school.
Pablo surveyed 130 students, and 10 of them preferred orange sherbet.
We can calculate the proportion of students who prefer orange sherbet in the sample:
\[ \text{Proportion of orange sherbet preference} = \frac{10}{130} \]
Now we can use this proportion to estimate the number of students in the entire school (528 students) who would prefer orange sherbet:
\[ \text{Estimated number of students in the school} = \text{Total students} \times \text{Proportion of orange sherbet preference} \]
\[ \text{Estimated number of students in the school} = 528 \times \frac{10}{130} \]
Calculating this, we first simplify \(\frac{10}{130}\):
\[ \frac{10}{130} = \frac{1}{13} \]
Now, we can multiply:
\[ \text{Estimated number of students} = 528 \times \frac{1}{13} = 528 \div 13 \approx 40.62 \]
Rounding to the nearest whole number gives us approximately 41 students.
Therefore, the estimated number of students in the school who prefer orange sherbet is 41.